Deltoidal icositetrahedral tegum

Deltoidal icositetrahedral tegum
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m2m4o3m
Elements
Cells	48 kite pyramids
Faces	48+48 scalene triangles, 24 kites
Edges	12+16+24+24+24
Vertices	2+6+8+12
Vertex figure	2 deltoidal icositetrahedra, 6+12 octahedra, 8 triangular tegums
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small rhombicuboctahedral prism
Conjugate	Great deltoidal icositetrahedral tegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	Yes
Nature	Tame

The deltoidal icositetrahedral tegum, also called the deltoidal icositetrahedral bipyramid, is a convex isochoric polychoron with 48 kite pyramids as cells. As the name suggests, it can be constructed as a tegum based on the deltoidal icositetrahedron.

In the variant obtained as the dual of the uniform small rhombicuboctahedral prism, if the short edges of the deltoidal icositetrahedron have length 1, its height is ${\sqrt {34+23{\sqrt {2}}}}\approx 8.15640$.