Hexakis tesseract

The hexakis tesseract, also known as the square-pyramidal tetracontoctachoron, is a convex isochoric polychoron with 48 square pyramids as cells. It can be obtained as the dual of the truncated hexadecachoron.

Hexakis tesseract
Rank4
TypeUniform dual
Notation
Coxeter diagramo4o3m3m ()
Elements
Cells48 square pyramids
Faces96 isosceles triangles, 24 squares
Edges32+64
Vertices8+16
Vertex figure8 cubes, 16 triakis tetrahedra
Measures (edge length 1)
Dichoral angle
Central density1
Related polytopes
DualTruncated hexadecachoron
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anywhere between and times that of the tesseract gives a fully symmetric variant of this polychoron.