Small snub distetracontoctablendic distetracontoctachoron

Small snub distetracontoctablendic distetracontoctachoron
(OFF file)
Rank	4
Type	Scaliform
Notation
Bowers style acronym	Sesdicabdic
Elements
Cells	96 tut as 48 tisso 288 tut 48 4tic 48 4cotco
Faces	1536 triangles 1536 hexagons 576 octagons 288 octagrams
Edges	5760
Vertices	1152
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {2}}}{2}}}\approx 1.79084$
Hypervolume	$194+240{\sqrt {2}}\approx 533.411$
Related polytopes
Army	Tispic
Regiment	Sesdicabdic
Conjugate	Great snub distetracontoctablendic distetracontoctachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The small snub distetracontoctablendic distetracontoctachoron or sesdicabdic is a scaliform polychoron. It consists of 96 truncated tetrahedra pairing up to form 48 truncated stellae octangulae, 288 more truncated tetrahedra, 48 blends of 4 truncated cubes, and 48 blends of 4 cuboctatruncated cuboctahedra. It can be formed as a blend of 24 tesseractihexadecatruncated tesseractihexadecachora.

Sesdicabdic's vertex coordinates are given by all permutations and sign changes of the following:

• ${\biggl (}\pm {\frac {1+{\sqrt {2}}}{2}},\pm {\frac {1+{\sqrt {2}}}{2}},\pm {\frac {{\sqrt {2}}-1}{2}},\pm {\frac {1}{2}}{\biggr )}$
• ${\biggl (}\pm {\frac {2+{\sqrt {2}}}{2}},\pm {\frac {{\sqrt {2}}-1}{2}},\pm {\frac {1}{2}},0{\biggr )}$
• ${\biggl (}\pm {\frac {4+{\sqrt {2}}}{4}},\pm {\frac {3{\sqrt {2}}}{4}},\pm {\frac {\sqrt {2}}{4}},\pm {\frac {\sqrt {2}}{4}}{\biggr )}$
• ${\biggl (}\pm {\frac {1+{\sqrt {2}}}{2}},\pm {\frac {\sqrt {2}}{2}},\pm {\frac {1}{2}},\pm 1{\biggr )}$
• ${\biggl (}\pm {\frac {2+3{\sqrt {2}}}{4}},\pm {\frac {2+{\sqrt {2}}}{4}},\pm {\frac {2-{\sqrt {2}}}{4}},\pm {\frac {2-{\sqrt {2}}}{4}}{\biggr )}$

External links

• Bowers, Jonathan. "Category S3: Special Scaliforms" (#S40).