Truncated tesseractic prism

Truncated tesseractic prism
File:Truncated tesseractic prism.png
Rank	5
Type	Uniform
Notation
Bowers style acronym	Tattip
Coxeter diagram	x x4x3o3o ()
Elements
Tera	16 tetrahedral prisms, 8 truncated cubic prisms, 2 truncated tesseracts
Cells	32 tetrahedra, 64 triangular prisms, 24 octagonal prisms, 16 truncated cubes
Faces	128 triangles, 32+96 squares, 48 octagons
Edges	64+64+192
Vertices	128
Vertex figure	Triangular pyramidal pyramid, edge lengths 1, √2+√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {3+{\sqrt {2}}}{2}}\approx 2.20711$
Hypervolume	${\frac {101+72{\sqrt {2}}}{6}}\approx 33.80390$
Diteral angles	Ticcup–trip–tepe: 120°
	Ticcup–op–ticcup: 90°
	Tat–tic–ticcup: 90°
	Tat–tet–tepe: 90°
Height	1
Central density	1
Number of external pieces	26
Level of complexity	20
Related polytopes
Army	Tattip
Regiment	Tattip
Dual	Tetrakis hexadecachoric tegum
Conjugate	Quasitruncated tesseractic prism
Abstract & topological properties
Flag count	15360
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B4×A1, order 768
Convex	Yes
Nature	Tame

The truncated tesseractic prism or tattip is a prismatic uniform polyteron that consists of 2 truncated tesseracts, 8 truncated cubic prisms, and 16 tetrahedral prisms. 1 truncated tesseract, 1 tetrahedral prism, and 3 truncated cubic prisms join at each vertex. As the name suggests, it is a prism based on the truncated tesseract, which also makes it a convex segmentoteron.

The truncated tesseracttic prism can be vertex-inscribed into the small rhombated penteract.

Vertex coordinates

The vertices of a truncated tesseractic prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Klitzing, Richard. "Tattip".