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In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U 38. It has 54 faces (30 squares , 12 pentagons and 12 pentagrams ), 120 edges and 60 vertices. [ 1 ] It is given a Schläfli symbol t 0,2 { 5 ⁄ 2 ,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron .
Rhombidodecadodecahedron_vertfig.png (600 × 600 pixels, file size: 15 KB, MIME type: image/png) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms.It additionally shares its edge arrangement with the rhombicosidodecahedron (having the square faces in common), and with the small dodecicosidodecahedron (having the decagonal faces in common).
Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet. Tessellations ... Rhombidodecadodecahedron; Small cubicuboctahedron;
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A shape with the same exterior appearance as the dodecadodecahedron can be constructed by folding up these nets: 12 pentagrams and 20 rhombic clusters are necessary. . However, this construction replaces the crossing pentagonal faces of the dodecadodecahedron with non-crossing sets of rhombi, so it does not produce the same internal st
It additionally shares its edges with the rhombidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the hexagonal faces in common). Convex hull