Abstract: An illumination system, in particular for illuminating tiled wall protrusions, includes at least one elongate, substantially U-shaped profile that has a base arm and two side arms projecting from the latter and arranged lying opposite one another, the first side arm being made longer than the second arm, at least one illuminant that is fastened or can be fastened within the receiving space defined by the base arm and the two side arms of the profile, and at least one elongate diffusion disc cover fastened or that can be fastened to the profile.

Abstract: A monitor display unit mounted on a surface and in electronic communication with a system or device to be monitored, comprising a face plate, a back plate having at least a portion of a side edge being translucent or transparent, a logic controller, and at least one light-emitting device in electronic communication with the controller. Actuation of the light-emitting device causes light to pass through the side edge of the back plate, thereby being visible to a viewer at an angle that can be generally parallel to the surface on which the display unit is mounted.

Abstract: A display wall includes a wall with at least one T-slot extending horizontally along a length of the wall. At least one display shelf is removably coupled with the wall through a respective T-slot and includes at least one support bracket for supporting the shelf when coupled with the wall. The at least one support bracket includes at least two electrical contacts electrically connected with at least one light positioned on the at least one display shelf. At least two electrical conductors are positioned within the respective T-slot and extend along a length thereof. The at least two electrical conductors electrically interconnect the electrical contacts with an electrical power source when the respective display shelf is coupled with the wall.

Abstract: A building block having at least one shape in the building block which includes a sealed volume surrounded by the shape, where the shape includes a transparent front and transparent rear to allow light to pass through the front and the rear and enter into a building partially or fully covered by the building block. There is at least one iris aperture diaphragm on the rear of each of at least one shape which is positioned to let all light pass into the building, each of the at least one iris aperture diaphragm having an adjustable opening to control how much light passes into the building.

Abstract: A wall wash lighting fixture includes a light source, a light pipe below the light source and a reflector offset from and surrounding the lower end of the light pipe. The lower end of the light pipe has an oblique, light-emitting face that provides uniform wall illumination up to a high vertical angle. The reflector faces substantially away from the wall and provides room-side illumination below about 45 vertical degrees. A preferred embodiment is suited for retrofit recessed installation, especially where small-aperture downlights are desired.

Abstract: A remotely controllable track lighting system includes a track with lamps supported on the track that are individually controlled by a wireless remote. Each lamp may be set to different intensity levels (e.g., high, mid, low, off) or to the same intensity level. All lamps may be set, upon initially turning on the lamps or at another time, to previously set intensity levels. The track system may also be powered via a wall switch where initially turning on the lamps via the wall switch causes all of the lamps to return to their previously set intensity levels or the user can move the wall switch off then on within a short period of time (e.g., 3 seconds) to cause all of the lamps to be set high.

Abstract: A linkable linear light emitting diode (LED) system provides apparatus and method for mechanically, optically, and electrically linking multiple LED modules disposed over a wide and separated area of a ceiling system. Openings can be cut in ceiling tiles of a drop ceiling system and the LED lighting modules are coupled to the tile through the opening, with the tile being sandwiched between different portions of the module. A remote driver system is placed within the drop ceiling above the tiles and provide multiple connectors for powering a multitude of lighting modules. Certain of the LED lighting modules include both input and output connectors for both receiving power or data and providing power or data to other modules. In this manner, some of the modules act as master LED lighting modules and those receiving power and/or data therefrom are act as slave modules.

Abstract: Devices, systems, and methods are provided for achieving desirable light distributions. In one exemplary embodiment, the light module includes a body having a pair of opposed complex parabolic bodies, an LED light source, and an inner reflective surface. The light source can be configured to provide for a desired light distribution, such as a bat wing light distribution. The provided light distribution can be such that it is not the result of passing light through a secondary optics component. Thus, while in some embodiments the LED module can include a glare reduction lens disposed over at least part of the LED light source, the lens may not affect the resulting light distribution configuration. Exemplary configurations of other systems, devices, kits, and methods associated with the teachings are also provided.

Abstract: Devices, systems, and methods are provided for both retrofitting existing lighting fixtures with LED panels and for installing ceiling tiles having LED modules incorporated therewith. In one exemplary embodiment, a thin panel includes an LED module integrated therewith and the panel is disposed over an opening in a troffer to provide light from the panel-module combination. In another exemplary embodiment, a ceiling tile includes an LED module integrated therewith and the tile is placed in a ceiling grid so light can be provided from that tile. Exemplary configurations of the systems, devices, and kits, as well as methods for installing the same, are also provided.

Abstract: The invention relates to an illumination device for a medical care unit. The illumination device comprises a plurality of light units arranged on a fixing unit to illuminate a room and a display area. At the same time, the color temperature and the distribution thereof as well as the brightness of the individual light units can be tuned to each other, for instance.

Abstract: A light fixture with co-formed plenum component is disclosed. Embodiments of the invention provide troffer-style recessed solid state fixture using a highly reflective plastic reflector. In at least some embodiments, the plastic reflector can meet the additional requirements placed on mechanical components exposed to the space above the ceiling plane in plenum return ceiling applications. Example embodiments include a light fixture with an LED light source and a reflector that is coextruded from a plenum rated substrate and a reflective material, for example, a plenum rated plastic substrate and a diffuse, white reflective material. In some embodiments, the plenum rated substrate includes polyetherimide, a polyphenylene ether/polystyrene blend, polycarbonate, polycarbonate copolymer, or a combination of the foregoing.

Abstract: According to one embodiment, a luminaire is provided which can enhance the feeling of brightness of a space and can reduce glare. The luminaire includes an equipment mounted on a ceiling surface. The equipment includes a light source and a light control unit. When an amount of light emitted outside from the equipment is an equipment luminous flux, and a direction right under the equipment has a luminous intensity distribution angle of 0°, the light control unit controls to cause a luminous flux falling within a range of a luminous intensity distribution angle of 90° to 120° to be 20% or more of the equipment luminous flux and to cause a luminous flux falling within a range of a luminous intensity distribution angle of 60° to 90° to be 20% or less of the equipment luminous flux.

Abstract: An LED-based light fixture that includes a light fixture housing forming a light emission aperture, one or more LEDs attached to a circuit board that is surrounded by the light fixture housing and emits light through the light emission aperture when powered. The LED-based light fixture further includes at least one flexible heat sink member that is thermally coupled with at least a portion of the circuit board and the light fixture housing.

Abstract: An LED downlight mounted onto a construction wall panel comprises a light source module and a heat sink holder. The light source module includes a light projection portion, a base to hold the light projection portion and a first coupling portion connected to the base. The heat sink holder includes a second coupling portion fastened to the first coupling portion and a first cooling portion formed on the outer surface of the heat sink holder and extended along the extension direction of the construction wall panel. The base and first cooling portion have respectively a first clamp surface corresponding to a decorative surface of the construction wall panel and a second clamp surface corresponding to a mask surface of the construction wall panel. The first and second clamp surfaces are respectively in contact with the decorative surface and mask surface to clamp the construction wall panel.

Abstract: Disclosed is a lighting fixture that provides approximately even illumination across a planar surface. Also enclosed is an LED light for producing the same. In one embodiment, the light fixture includes a plurality of hollow gradient diffusion globes; each diffusion globe is affixed to a planar reflector that forms an outer illumination surface of the light fixture. Each diffusion globe surrounds a light-emitting portion of an LED or LED cluster. The hollow gradient diffusion globe can include a wall defining by the interior and exterior boundary of the diffusion globe. The wall includes diffusing-particulate homogenously distributed within the wall that in combination with varying thickness of the wall creates continuously varying diffusion. The relative spacing of the diffusion globes on the planar reflective surface in combination with the continuous variable diffusion property of each globe produce approximately even illumination across the outer illumination surface of the LED light fixture.

Abstract: An open bulb fixture is a lighting fixture presenting a light bulb exposed and unprotected to an area around the light bulb. A light cover is a transparent or translucent cover protecting a light bulb while permitting light from the light bulb to pass through the light cover to the area around the light bulb. A method for protecting an open bulb lighting fixture includes positioning a light cover to the open bulb fixture.

Abstract: A curtain wall having integrated lighting, comprises a first series of transoms (14), a second series of mullions (12), at least one of the first transoms and the second mullions having an extruded first member (20) having a hollow interior, a driver (30) positioned within the hollow portion of the first member, a second member (22) connected to the first member, the second member having a lens (46) disposed along an outer side of the second member to illuminate one of an outer façade of a building or an area adjacent said façade.

Abstract: There is provided a low bay lighting apparatus secured to an elevated horizontal surface. The low bay lighting apparatus including a light fixture and a mounting bracket to which the light fixture is to be removable attached. The light fixture includes a plurality of posts disposed on opposite ends of opposing outer side surfaces of the light fixture. The mounting bracket includes a plurality of slots configured to mate respectively with the plurality of posts to removably secure the light fixture to the mounting bracket. When being serviced, the light fixture is configured to freely hang from a first set of slots.

Abstract: An LED or fluorescent recessed lighting fixture having a pair of aligned LED boards or a pair of fluorescent bulbs each shielded by a diffuser. Each diffuser is retained by an angled wall and a portion of a V-shaped diffuser cover. The apparatus includes light emitted from a light source toward the location where the light is to illuminate the area. A reflector assembly is set in a straight line at an angle in the range of 45 degrees. A lens covers the light source and is retain by a portion of the reflector and a V-shaped basket.

Abstract: An improved light emitting diode (LED) illuminating assembly is provided with a multiple sided LED lighting bar, also referred to as a multi-sided LED light bar, comprising a non-curvilinear LED luminary for enhanced LED lighting. The LED illuminating assembly can be used for overhead ceiling lighting, menu boards and other LED illuminating signs, as well as for other uses.

Abstract: A recessed lighting fixture which utilizes a fluorescent light source. The fluorescent lights are shrouded by a diffuser lens basket so that light from the fluorescent bulbs shining through the diffuser is dispersed to reduce glare and visibility of the source of light. It is an object of the present invention to provide a fluorescent recessed lighting fixture which has the illumination from the fluorescent bulbs shining through a diffuser. It is also an object of the present invention to provide a single driver or ballast within the body of the fixture where access can only be gained from below the fixture.

Abstract: Proposedis a remote control device (100), arranged to control a lighting system(1). The lighting system comprises a plurality of light-modules (10) capable of emitting modulated light comprising light module identification codes (20). The remote controldevice (100) comprises a sensor (110) arranged to switch the light modules (10) from an operational mode (210) in which the light emitted by the light modules (10) is non-5 modulated to a control mode (230) in which the light emitted by the light modules (10) is modulated. Advantageously, the invention provides a lighting system with improved energy efficiency and EMC characteristics.

Abstract: The invention is a renewable energy powered light assembly for a roof window of a building. A housing extends within the roof aperture from an interior of the house towards the exterior. A plurality of lighting elements is disposed in the housing. A renewable energy source is connected to each of the lighting elements. A solar panel array collects light from an electrical grid powered lighting element. A rechargeable power source is connected to the renewable energy source and the plurality of lighting elements. The invention also is a light assembly for illuminating an area from a floor of a building. A renewable energy source is externally mounted and coupled to a plurality of lighting elements disposed adjacent the floor. A rechargeable power source is coupled to the energy source and the plurality of lighting elements for storing the power generated and powering the plurality of lighting elements.

Abstract: A lighting device such as a solid state downlight includes a lens structure with at least one integrally formed trim retaining element, and a trim structure including at least one lens structure engaging element, wherein the at least one lens structure engaging element is arranged to removably engage the least one trim retaining element, such as by rotating the trim structure. A generally cylindrical portion of the trim structure may be arranged to surround a central portion of the lens structure, thereby reducing or eliminating light piping and eliminating visible attachment elements for the trim structure.

Abstract: A luminaire includes a light-emitting element, a side surface cover, a lower surface cover, a diffuser, and a prism, which is an example of an optical member. The light-emitting element emits light. The side surface cover is arranged a predetermined distance from the light-emitting element. The light emitted by the light-emitting element is transmitted through the side surface cover. The lower surface cover is provided at the lower end of the side surface cover. The light emitted by the light-emitting element is transmitted through the lower surface cover. The diffuser is a member provided between the lower surface cover and the light-emitting element to diffuse the light emitted by the light-emitting element. The prism adjusts a traveling direction of the light transmitted through the side surface cover to be different from a traveling direction of the light emitted by the light-emitting element and transmitted through the lower surface cover.

Abstract: A two-component light fixture that includes a passive component and an active component is disclosed. In some embodiments, the active component is recessed within a ceiling or wall and the passive component is positioned below the active component. The active component emits light towards the passive component, which includes an optical element that can redirect the light by scattering, reflection, refraction, diffusion, total internal reflection and/or dispersion.

Abstract: Example embodiments relate to a lighting device comprising a shell, at least one LED positioned at the bottom of the shell, and at least one fixing mechanics. The fixing mechanics comprises a base and a fixing element. An end of the base forms a plurality of pins which is ended with a hook. The fixing element connected with the base is fixed on the bottom of the shell.

Abstract: A luminaire includes a heat spreader; a heat sink; an LED light source; a power supply; an electrical supply line having a first end connected to the power supply, and a second end connected to a plug-in connector; and, an optic securely retained relative to the heat spreader or heat sink. An accessory kit includes a first pre-wired jumper including a pair of insulated electrical wires having a first plug-in connector electrically connected at one end and an Edison base electrically connected at the other end; and/or, a second pre-wired jumper including a pair of insulated electrical wires having a second plug-in connector electrically connected at one end and unconnected wire ends at the other end. The plug-in connector of the first pre-wired jumper and the second pre-wired jumper are each configured to electrically engage with the plug-in connector of the electrical supply line.

Abstract: A lamp and a hardscape structure illuminated by the lamp are disclosed. The lamp is formed from a plate to which a light fixture is attached. The plate may have a flange, a decorative face plate and side panels attached to direct light from the fixture along the hardscape on which the lamp is mounted. Mounting is effected by positioning the plate between discrete hardscape elements that are stacked one atop another. A portion of the plate projects out from the structure allowing the fixture to cast light on the structure surface. A light transmitting cover is also provided.

Abstract: Combination light diffusion with either sound diffusion or absorption is provided in a single lighting fixture, to provide uniform luminosity and sound control. The traditional flat light diffuser is replaced with a translucent acoustical element which either diffuses sound or absorbs the sound. The sound diffuser topology includes random surfaces, geometrical shapes, number theoretic diffusers or optimized rectilinear or curvilinear surfaces. The translucent sound absorber includes microperforated or microslit panels, as well as translucent fabrics and microperforated, translucent wood veneers.

Abstract: A downlight fixture includes an optic housing, a light-emitting diode (LED) array, and a lens-less reflector. The LED array emits directional light rays in a downward direction towards an illuminated target. The reflector is mounted within the optic housing and adjacent to the LED array. The reflector has a hyperbolic wall continuously extending between a narrow neck and a wide bell. The light rays are spread into a light beam within the reflector upon making contact solely with the hyperbolic wall.

Abstract: An adapter structure which cooperates between a modular electrical distribution unit and a light fixture to facilitate electrical connection therebetween. The adapter structure includes an adapter module having an insulative housing containing electrical conductors extending therethrough and defining connectors at input and output ends thereof. The housing mounts directly to the light fixture, preferably within and extending through a knock-out port in a wall of the light fixture, and a plug-type connector at the output end of the adapter structure can be plug engaged with a compatible connector associated with a electrical power distribution unit. The output end of the adapter has a gripping conductive socket structure which enables pigtail conductors associated with the light fixture to be directly plugged therein.

Abstract: Disclosed is a lighting system and a method to change the internal light source of the lighting system, wherein maintenance and aesthetic considerations make it necessary to access the internal light source solely from the front of the lighting system without moving or removing a sign face. Access, in part, is provided by a light baffle track system inside the light system that turns a flexible light baffle (i.e., the light source) within the service box from a substantially vertical orientation to a substantially horizontal orientation as the flexible light baffle is removed and reinstalled through the service box and front access door. The flexible light baffle and light baffle track system work in concert to efficiently turn the flexible light baffle solely within the service box such that the height and depth of the service box is minimized.

Abstract: A switch panel illumination structure for mounting to an outer side of an indoor switch includes a panel provided with a receptacle, and an illumination mechanism detachably received in the receptacle. A conductive section is disposed in the receptacle and electrically connected to an AC/DC conversion module. The illumination mechanism has a first and a second light-emitting section electrically connected to an illumination control module thereof, and the illumination control module is electrically connected to the AC/DC conversion module via contacts and the conductive section. The illumination mechanism further has a switch section electrically connected to the first and second light-emitting sections and the illumination control module. The illumination mechanism can be securely located in the receptacle to serve as a night lamp or an emergency light or be easily removed from the receptacle for use as a flashlight without changing the appearance and the size of the panel.

Abstract: An electrical wiring device includes a dimmable night light therein. The night light includes one or more light sources for emitting light and an optional lens disposed over the light sources. The lens allows light from the light sources to be emitted therethrough. In some embodiments, the lens is used to turn on the night light, turn off the night light, and dim the night light. In some exemplary embodiments, manipulation of the lens selects an operating mode for the device. The device optionally includes an occupancy detection sensor to assist detecting occupancy within a monitored area.

Abstract: An lighting fixture includes a reflector, a pedestal, and a lighting module. The reflector includes an opening formed therethrough and the pedestal is positioned in communication with the opening. The lighting module is coupled to the pedestal. In certain embodiments, the reflector is organically shaped and includes four parts, where each part is substantially S-shaped. The lighting module includes a frame and indirect LEDs that emit light toward the interior surface of the reflector. The indirect LEDs are positioned below the lowest portions of the reflector a are positioned at an angle with respect to a horizontal axis. The frame includes a cut-off wall that provides for a cut-off angle for the indirect LEDs and one or more fins. The frame and the pedestal provide thermal management for the LEDs. In certain embodiments, the lighting module also includes one or more of direct LEDs and an active cooling module.

Abstract: A low-voltage LED lighting system, LED lighting fixtures, and a method for installation thereof in which the system includes: (a) at least one LED lighting fixture each having one or more LEDs; (b) at least one remotely-located power driver; and (c) interconnections between the at least one LED fixture and the at least one driver using communication network cabling and standard 8P8C network connectors. Preferred lighting fixtures are recessed lighting fixtures adapted for ceiling mounting.

Abstract: This invention relates to a light emitting device (100) having a movable collimating unit for adjusting the output direction of light being emitted from the light emitting device. The light emitting device comprises a base unit (110), and a light output unit (120) which is engaged with the base unit. The light output unit comprises at least one light source (121) for emitting light. The light emitting device further comprises a movably arranged collimating unit (130) for adjusting the direction of the emitted light, which is arranged such that it encompasses a light output portion (125), which is arranged on the light output unit.

Abstract: A solid state, bidirectional light sheet and method of fabricating the sheet are disclosed. In one embodiment, bare LED chips have top and bottom electrodes, where the bottom electrode is a large reflective electrode. An array of LEDs (e.g., 500 LEDs) is sandwiched between at least two transparent substrates having conductors bonded to the electrodes without wires. Various ways to connect the LEDs in series are described along with various embodiments. The light sheets are formed to emit light from opposite surfaces of the light sheet to create a bidirectional light sheet. The light sheet may be suspended from a ceiling to be perpendicular to the ceiling, or the angles of the light sheet may be adjusted. The suspended light sheet may form a cylinder for uniform illumination of the floor and ceiling. Lenses may be formed in the light sheet to emit light at any peak intensity angle to achieve any light emission pattern.

Abstract: This disclosure provides systems, methods and apparatus for providing a desired illumination pattern within a given plane. In one aspect, a light wash system can be configured to provide substantially even illumination on a wall or floor. The light wash system can use light-shaping optics such as a stack of optical films to provide a light wash system which is smaller than conventional light wash systems which utilize parabolic reflectors. The light wash system may include an internal retroreflector to allow a wider range of throw distances for the light wash system.

Abstract: The lighting device comprises a case comprising: a bottom plate; a first wall extending from the bottom plate; a second wall extending from the bottom plate and facing to the first wall; a first top plate extending perpendicular to the first wall; and a second top plate extending perpendicular to the second wall, a light emitter disposed on the bottom plate of the case; and a diffuser plate spaced apart from the light emitter and disposed between the first wall and the second wall, wherein the first wall and the second wall comprise a coupling recess, and wherein the diffuser plate is coupled to the coupling recess.

Abstract: A wall wash lighting fixture includes a light source, a light pipe below the light source and a reflector offset from and surrounding the lower end of the light pipe. The lower end of the light pipe has an oblique, light-emitting face that provides uniform wall illumination up to a high vertical angle. The reflector faces substantially away from the wall and provides room-side illumination below about 45 vertical degrees. A preferred embodiment is suited for retrofit recessed installation, especially where small-aperture downlights are desired.

Abstract: A linkable linear light emitting diode (LED) system provides apparatus and method for mechanically, optically, and electrically linking multiple LED modules disposed over a wide and separated area of a ceiling system. Openings can be cut in ceiling tiles of a drop ceiling system and the LED lighting modules are coupled to the tile through the opening, with the tile being sandwiched between different portions of the module. A remote driver system is placed within the drop ceiling above the tiles and provide multiple connectors for powering a multitude of lighting modules. Certain of the LED lighting modules include both input and output connectors for both receiving power or data and providing power or data to other modules. In this manner, some of the modules act as master LED lighting modules and those receiving power and/or data therefrom are act as slave modules.

Abstract: This is directed to a luminaire having a removable inner accessory and optical component. A luminaire can include a base and an outer accessory through which light generated by a light source placed in the base is transmitted. To customize the light emitted by the luminaire, an inner accessory having an optical component can be placed within the outer accessory. The optical component can be tuned to provide a light pattern corresponding to an environment in which the luminaire is placed. Because all of the components used to create the luminaire, other than the optical component, are standard, the luminaire can be easily constructed with a default optical component, but also easily customized at a minimal cost. In addition, the optical component can be recessed relative to the outer accessory to improve optical performance of the luminaire.

Abstract: Lighting apparatus and structures are described to space electrical drivers from a light panel. In this way, a driver box housing the driver can be spaced from the light panel to communicate with pre-existing facilities (e.g. electrical wiring) and can serve the additional advantage of keeping the driver box out of standing water that may accumulate on the structure.

Abstract: An LED downlight mounted onto a construction wall panel comprises a light source module and a heat sink holder. The light source module includes a light projection portion, a base to hold the light projection portion and a first coupling portion connected to the base. The heat sink holder includes a second coupling portion fastened to the first coupling portion and a first cooling portion formed on the outer surface of the heat sink holder and extended along the extension direction of the construction wall panel. The base and first cooling portion have respectively a first clamp surface corresponding to a decorative surface of the construction wall panel and a second clamp surface corresponding to a mask surface of the construction wall panel. The first and second clamp surfaces are respectively in contact with the decorative surface and mask surface to clamp the construction wall panel.

Abstract: Some embodiments provide a fenestration apparatus including at least one glazing pane capable of being installed in an opening of a building envelope and a tessellated structure disposed adjacent to the at least one glazing pane. The tessellated structure can include at least one partition having a first face and a second face. The at least one partition can define a plurality of spatially separated cells within a substantially contiguous region of the opening. Each of the plurality of spatially separated cells can have a cell width and a cell depth. Each of the plurality of spatially separated cells can be at least partially surrounded by the first face of the at least one partition, the second face of the at least one partition, or a combination of the first face and the second face of the at least one partition.

Abstract: An LED downlight provides a more evenly distributed light output. The LED downlight includes an LED light source, such as one or more LEDs, LED die packages, or LED chip on board modules, an upper reflector, a lower reflector disposed below the upper reflector, and a lens disposed between the upper reflector and the lower reflector. The lens includes several features that help disperse light emitted by the LED light source. The lens includes a diffusion element, such as a pigment, bulk scattering, prismatic, inlays, or another method for diffusing light through a lens. The lens is curved in a concave manner when viewed from the light source. The curve of the lens can be tangent to the physical cutoff of the lower reflector to more evenly distribute light emitted by the LED light source and to improve the visual effect of an evenly luminous lens.

Abstract: A light apparatus is mounted to a surface of a building. The apparatus has at least one elongate mounting extrusion engaged to the surface. At least one elongate trim extrusion is mounted to the mounting extrusion and extending forward therefrom. The trim extrusion has a forward edge and an upwardly and rearwardly sloping surface extending from the edge. At least one light source is mounted to at least one of the mounting extrusion and trim extrusion.

Abstract: An LED lighting apparatus includes a support unit including a support surface facing an illumination side, a plurality of LED chips supported on the support surface, and a cover that covers the support surface and transmits light from the LED chips. The cover includes a periphery which, as viewed in plan, includes four first sides that are spaced apart from each other and four second sides each connecting ends of adjacent ones of the first sides. The first sides consisting of two pairs of parallel sides, and each of the first sides constituting one of the two pairs and each of the first sides constituting the other one of the two pairs form a right angle. Each of the first sides and each of the adjacent second sides form an obtuse angle.