Steriruncitruncated 6-cube

Steriruncitruncated 6-cube

Rank	6
Type	Uniform
Notation
Bowers style acronym	Captix
Coxeter diagram	x4x3o3x3x3o ()
Elements
Peta	12 steriruncitruncated 5-cubes 64 runcicantellated 5-simplices 192 decachoric prisms 240 octagonal-truncated tetrahedral duoprisms 160 triangular-truncated cubic duoprisms
Tera	1280 triangular duoprisms 720 triangular-octagonal duoprisms 960 hexagonal-octagonal duoprisms 2880 truncated tetrahedral prisms 480 truncated cubic prisms 384 decachora 384 prismatorhombated pentachora 60 prismatorhombated hexadecachora
Edges	40320
Vertices	11520
Vertex figure	Irregular square tettene
Measures (edge length 1)
Circumradius	${\sqrt {\frac {27+10{\sqrt {2}}}{2}}}\approx 4.53553$
Hypervolume	${\frac {789041+550290{\sqrt {2}}}{90}}\approx 17414.09535$
Central density	1
Related polytopes
Army	Captix
Regiment	Captix
Abstract & topological properties
Flag count	11059200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B₆, order 46080
Flag orbits	240
Convex	Yes
Nature	Tame

The steriruncitruncated 6-cube (OBSA: captix), also called the steriruncitruncated dodecapeton, or celliprismatotruncated hexeract is a convex uniform 6-polytope. It consists of 12 steriruncitruncated 5-cubes, 64 runcicantellated 5-simplices, 192 decachoric prisms, 240 octagonal-truncated tetrahedral duoprisms, and 160 triangular-truncated cubic duoprisms. 2 steriruncitruncated 5-cubes, 1 runcicantellated 5-simplex, 1 decachoric prism, 2 octagonal-truncated tetrahedral duoprisms, and 1 triangular-truncated cubic duoprism join at each vertex. As the name suggests, it is the steriruncitruncation of the 6-cube.

Vertex coordinates[edit | edit source]

The coordinates of a steriruncitruncated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:

$\left(\pm {\frac {1+3{\sqrt {2}}}{2}},\,\pm {\frac {1+3{\sqrt {2}}}{2}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right)$ .

Gallery[edit | edit source]

B₅ orthographic projection
B₄
B₃
B₂
A₅
A₃

External links[edit | edit source]

Wikipedia contributors. "Steriruncitruncated 6-cube".

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram
6-cube	ax	${4,3,3,3,3}$
Rectified 6-cube	rax	r ${4,3,3,3,3}$
Birectified 6-cube	brox	t₂ ${4,3,3,3,3}$
Birectified 6-orthoplex	brag	t₂ ${3,3,3,3,4}$
Rectified 6-orthoplex	rag	r ${3,3,3,3,4}$
6-orthoplex	gee	${3,3,3,3,4}$
Truncated 6-cube	tox	t ${4,3,3,3,3}$
Cantellated 6-cube	srox	rr ${4,3,3,3,3}$
Runcinated 6-cube	spox	t_0,3 ${4,3,3,3,3}$
Stericated 6-cube	scox	t_0,4 ${4,3,3,3,3}$
Pentellated 6-cube	stoxog	t_0,5 ${4,3,3,3,3}$
Bitruncated 6-cube	botox	t_1,2 ${4,3,3,3,3}$
Bicantellated 6-cube	saborx	t_1,3 ${4,3,3,3,3}$
Biruncinated 6-cube	sobpoxog	t_1,4 ${4,3,3,3,3}$
Stericated 6-orthoplex	scag	t_0,4 ${3,3,3,3,4}$
Tritruncated 6-cube	xog	t_2,3 ${4,3,3,3,3}$
Bicantellated 6-orthoplex	siborg	t_1,3 ${3,3,3,3,4}$
Runcinated 6-orthoplex	spog	t_0,3 ${3,3,3,3,4}$
Bitruncated 6-orthoplex	botag	t_1,2 ${3,3,3,3,4}$
Cantellated 6-orthoplex	srog	rr ${3,3,3,3,4}$
Truncated 6-orthoplex	tag	t ${3,3,3,3,4}$
Cantitruncated 6-cube	grox	tr ${4,3,3,3,3}$
Runcitruncated 6-cube	potax	t_0,1,3 ${4,3,3,3,3}$
Steritruncated 6-cube	catax	t_0,1,4 ${4,3,3,3,3}$
Pentitruncated 6-cube	tacog	t_0,1,5 ${4,3,3,3,3}$
Runcicantellated 6-cube	prox	t_0,2,3 ${4,3,3,3,3}$
Stericantellated 6-cube	crax	t_0,2,4 ${4,3,3,3,3}$
Penticantellated 6-cube	topag	t_0,2,5 ${4,3,3,3,3}$
Steriruncinated 6-cube	copox	t_0,3,4 ${4,3,3,3,3}$
Penticantellated 6-orthoplex	tapox	t_0,2,5 ${3,3,3,3,4}$
Pentitruncated 6-orthoplex	tacox	t_0,1,5 ${3,3,3,3,4}$
Bicantitruncated 6-cube	gaborx	t_1,2,3 ${4,3,3,3,3}$
Biruncitruncated 6-cube	boprag	t_1,2,4 ${4,3,3,3,3}$
Steriruncinated 6-orthoplex	copog	t_0,3,4 ${3,3,3,3,4}$
Biruncitruncated 6-orthoplex	boprax	t_1,2,4 ${3,3,3,3,4}$
Stericantellated 6-orthoplex	crag	t_0,2,4 ${3,3,3,3,4}$
Steritruncated 6-orthoplex	catog	t_0,1,4 ${3,3,3,3,4}$
Bicantitruncated 6-orthoplex	gaborg	t_1,2,3 ${3,3,3,3,4}$
Runcicantellated 6-orthoplex	prog	t_0,2,3 ${3,3,3,3,4}$
Runcitruncated 6-orthoplex	potag	t_0,1,3 ${3,3,3,3,4}$
Cantitruncated 6-orthoplex	grog	tr ${3,3,3,3,4}$
Runcicantitruncated 6-cube	gippox	t_0,1,2,3 ${4,3,3,3,3}$
Stericantitruncated 6-cube	cagorx	t_0,1,2,4 ${4,3,3,3,3}$
Penticantitruncated 6-cube	togrix	t_0,1,2,5 ${4,3,3,3,3}$
Steriruncitruncated 6-cube	captix	t_0,1,3,4 ${4,3,3,3,3}$
Pentiruncitruncated 6-cube	tocrag	t_0,1,3,5 ${4,3,3,3,3}$
Pentisteritruncated 6-cube	tactaxog	t_0,1,4,5 ${4,3,3,3,3}$
Steriruncicantellated 6-cube	coprix	t_0,2,3,4 ${4,3,3,3,3}$
Pentiruncicantellated 6-cube	tiprixog	t_0,2,3,5 ${4,3,3,3,3}$
Pentiruncitruncated 6-orthoplex	tocrax	t_0,1,3,5 ${3,3,3,3,4}$
Penticantitruncated 6-orthoplex	togrig	t_0,1,2,5 ${3,3,3,3,4}$
Biruncicantitruncated 6-cube	gobpoxog	t_1,2,3,4 ${4,3,3,3,3}$
Steriruncicantellated 6-orthoplex	coprag	t_0,2,3,4 ${3,3,3,3,4}$
Steriruncitruncated 6-orthoplex	captog	t_0,1,3,4 ${3,3,3,3,4}$
Stericantitruncated 6-orthoplex	cagorg	t_0,1,2,4 ${3,3,3,3,4}$
Runcicantitruncated 6-orthoplex	gopog	t_0,1,2,3 ${3,3,3,3,4}$
Steriruncicantitruncated 6-cube	gocax	t_0,1,2,3,4 ${4,3,3,3,3}$
Pentiruncicantitruncated 6-cube	tagpox	t_0,1,2,3,5 ${4,3,3,3,3}$
Pentistericantitruncated 6-cube	tocagrax	t_0,1,2,4,5 ${4,3,3,3,3}$
Pentistericantitruncated 6-orthoplex	tecagorg	t_0,1,2,4,5 ${3,3,3,3,4}$
Pentiruncicantitruncated 6-orthoplex	tagpog	t_0,1,2,3,5 ${3,3,3,3,4}$
Steriruncicantitruncated 6-orthoplex	gocog	t_0,1,2,3,4 ${3,3,3,3,4}$
Omnitruncated 6-cube	gotaxog	t_0,1,2,3,4,5 ${4,3,3,3,3}$

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Steriruncitruncated 6-cube

Vertex coordinates[edit | edit source]

Gallery[edit | edit source]

External links[edit | edit source]

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