5. Anomalous convex uniform polychoron


[Not Wythoffian; no Coxeter-Dynkin graph]
Grand antiprism [47]
Alternative names:
Pentagonal double antiprismoid (Norman W. Johnson)
Gap (Jonathan Bowers: for grand antiprism)

Symmetry group: The ionic diminished Coxeter group [[10,2+,10]], of order 400

Schläfli symbol: s{5}.s{5} (extended)

Elements:
Cells: 20 pentagonal antiprisms, 300 tetrahedra
Faces: 700 triangles (200 joining pentagonal antiprisms to tetrahedra, 500 joining tetrahedra to tetrahedra), 20 pentagons (all joining pentagonal antiprisms to pentagonal antiprisms)
Edges: 500
Vertices: 100

Vertex figure:Dissected Regular Icosahedron
“Dissected regular icosahedron”: a regular icosahedron in which a patch of 8 triangles is replaced by a pair of trapezoids, edge lengths tau, 1, 1, 1, joined together along their edge of length tau, to give a tetradecahedron whose faces are the 2 trapezoids and the 12 remaining equilateral triangles


Click on the underlined text to access various portions of the Convex Uniform Polychora List:

Four Dimensional Figures Page: Return to initial page

Nomenclature: How the convex uniform polychora are named

List Key: Explanations of the various List entries

Multidimensional Glossary: Explanations of some geometrical terms and concepts

Section 1: Convex uniform polychora based on the pentachoron (5-cell): polychora #1–9

Section 2: Convex uniform polychora based on the tesseract (hypercube) and hexadecachoron (16-cell): polychora #10–21

Section 3: Convex uniform polychora based on the icositetrachoron (24-cell): polychora #22–31

Section 4: Convex uniform polychora based on the hecatonicosachoron (120-cell) and hexacosichoron (600-cell): polychora #32–46

Section 6: Convex uniform prismatic polychora: polychora #48–64 and infinite sets

Section 7: Uniform polychora derived from glomeric tetrahedron B4: all duplicates of prior polychora