Sidtid-facetings
In the sidtid (small ditrigonal icosidodecahedron, sid-12-20-0-0) there are 12 pentagrams and 20 triangles. It has 6 5-fold and 10 3-fold rotation axis. The edges of the sidtid can be connected by pentagrams (first number), triangles (second number), squares (third number) and pentagons (fourth number). So 159 polyhedra (and several compounds) are created, which are grouped in the following way: 46 pyramidal and 7 antiprismatic polyhedra have a 5-fold axis, 76 pyramidal and 6 antiprismatic figures have a 3-fold axis. Furthermore there are 22 chiral polyhedra with a 3-fold axis in the sidtid-regiment, 6 of them have an antiprismatic and 15 have a pyramidal structure, one polyhedron is tetrahedral-chiral. The cube and several cube-compounds are sidtid-facetings too. There are four figures with icosahedral symmetry: the compound of 5 cubes, the great ditrigonal icosidodecahedron (gidtid), the ditrigonal dodecadodecahedron (didtid) and sidtid itself.
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sidtid-facetings by R. Klitzing:
