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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 .
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).
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.
Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet. Tessellations ... Rhombidodecadodecahedron; Small cubicuboctahedron;
3D model of a nonconvex great rhombicosidodecahedron. In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U 67.It has 62 faces (20 triangles, 30 squares and 12 pentagrams), 120 edges, and 60 vertices. [1]
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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