Abstract: The present invention relates to assemblable symmetrical bodies consisting of a regular central body (1-5, 6-8, 26) and a multitude of partly congruent covering pieces (9, 23). Fasteners (18, 19) are firmly fixed to the central body (1-5, 6-8, 26), or to the basic surface (10) of each of the covering pieces (9, 23) respectively, providing a relatively firm connection between the regular central body (1-5, 6-8, 26) and the covering pieces (9, 23) which can be broken and re-established as often as desired using relatively little force. The covering pieces (9, 23) may be shaped like jigsaw puzzle pieces (27, 28) containing projections (34) and matching cut-outs (31).