Retrosnub disicositetrachoron
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Retrosnub disicositetrachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Rasdi 
Coxeter diagram  
Elements  
Cells  24+96 tetrahedra, 24 great icosahedra 
Faces  96+96+288 triangles 
Edges  144+288 
Vertices  96 
Vertex figure  Trireplenished great icosahedron, edge length 1 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Gike–3–gike: 120° 
Tet–3–tet:  
Gike–3–tet:  
Central density  23 
Number of external pieces  9024 
Level of complexity  974 
Related polytopes  
Army  Sadi 
Regiment  Rasdi 
Conjugate  Snub disicositetrachoron 
Abstract & topological properties  
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  F_{4}/2, order 576 
Convex  No 
Nature  Tame 
The retrosnub disicositetrachoron, or rasdi, is a nonconvex uniform polychoron that consists of 24+96 regular tetrahedra and 24 great icosahedra. 5 tetrahedra and 3 great icosahedra join at each vertex.
It is related to the grand hexacosichoron in a similar way as the snub disicositetrachoron is to the regular hexacosichoron, with the great icosahedra being vertex figures of the grand hexacosichoron.
Gallery[edit  edit source]

Wireframe

Convex core, with 24 tetrahedra and 96 gyroelongated triangular pyramids
Vertex coordinates[edit  edit source]
The vertices of a retrosnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:
Related polychora[edit  edit source]
The retrosnub disicositetrachoron's regiment also contains a coincidic scaliform polychoron, the icositetradiminished great faceted hexacosichoron.
External links[edit  edit source]
 Bowers, Jonathan. "Category 20: Miscellaneous" (#970).
 Klitzing, Richard. "rasdi".