Hexadecahemidecateron

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Hexadecahemidecateron
Hehad.PNG
Rank5
TypeUniform
SpaceSpherical
Bowers style acronymHehad
Coxeter diagramCDel nodeb 1.pngCDel 3b.pngCDel label3-2.pngCDel branch.pngCDel 3ab.pngCDel branch.png/2 ((x3o3o3o3o3/2*b)/2)
Elements
Vertex figureTesseractihemioctachoron, edge length 1
Tera16 pentachora, 5 hexadecachora
Cells80 tetrahedra
Faces80 triangles
Edges40
Vertices10
Measures (edge length 1)
Circumradius
Dichoral angle
Related polytopes
ArmyTac
RegimentTac
CompanyTac
DualHexadecahemidecacron
ConjugateNone
Topological properties
OrientableNo
Properties
SymmetryD5, order 192
ConvexNo
NatureTame

The hexadecahemidecateron, or hehad, is a uniform hemipolyteron. It has 16 regular pentachora and 5 central hexadecachora as facets, with 8 pentachora and 4 hexadecachora at each vertex in the form of a tesseractihemioctachoron. It is the 5D demicross.

It is a faceting of the triacontaditeron, analogous to how the tetrahemihexahedron is a faceting of the octahedron, and the tesseractihemioctachoron is a faceting of the hexadecachoron. It shares the triacontaditeron's vertices, edges, faces, and cells. The 16 pentachora are half of those of the triacontaditeron, while the hexadecachora are its original vertex figures.

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