Runcicantitruncated 6-orthoplex

Runcicantitruncated 6-orthoplex

Rank	6
Type	Uniform
Notation
Bowers style acronym	Gopog
Coxeter diagram	o4o3x3x3x3x ()
Elements
Peta	12 cantitruncated 5-orthoplexes 64 runcicantitruncated 5-simplices 60 truncated hexadecachoric prisms 160 hexagonal-octahedral duoprisms
Tera	1280 triangular-hexagonal duoprisms 480+480 octahedral prisms 960 truncated tetrahedral prisms 384 great rhombated pentachora 120 truncated hexadecachora 192 great prismatodecachora
Cells	3840+3840 triangular prisms 960 octahedra 1920+1920 hexagonal prisms 1920 truncated tetrahedra 960+240 truncated octahedra
Faces	7680 triangles, 5760+5760+1440 squares, 3840+960+960 hexagons
Edges	11520+2880+2880+2880
Vertices	5760
Vertex figure	Irregular square tettene
Measures (edge length 1)
Circumradius	${\sqrt {15}}\approx 3.87298$
Hypervolume	${\frac {707669}{90}}\approx 7862.98889$
Central density	1
Related polytopes
Army	Gopog
Regiment	Gopog
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B₆, order 46080
Convex	Yes
Nature	Tame

The runcicantitruncated 6-orthoplex, also called the runcicantitruncated hexacontatetrapeton, great prismated hexacontatetrapeton, or gopog, is a convex uniform 6-polytope. It consists of 12 cantitruncated 5-orthoplexes, 64 runcicantitruncated 5-simplices, 60 truncated hexadecachoric prisms, and 160 hexagonal-octahedral duoprisms. 1 cantitruncated 5-orthoplex, 4 runcicantitruncated 5-simplex, 1 truncated hexadecachoric prism, and 1 hexagonal-octahedral duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the 6-orthoplex.

Vertex coordinates[edit | edit source]

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

$\left(\pm 2{\sqrt {2}},\,\pm {\frac {3{\sqrt {2}}}{2}},\,\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0\right).$

Representations[edit | edit source]

A runcicantitruncated 6-orthoplex has the following Coxeter diagrams:

o4o3x3x3x3x () (full symmetry)
o3x3x3x3x *b3o () (D₆ symmetry)

Gallery[edit | edit source]

B₅ orthographic projection
B₄
B₃
B₂
A₅
A₃

External links[edit | edit source]

Klitzing, Richard. "gopog".

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 ${4,3,3,3,3}$

v t e truncations
Name	OBSA	CD diagram
6-demicube	hax
Birectified 6-cube	brox
Birectified 6-orthoplex	brag
Rectified 6-orthoplex	rag
6-orthoplex	gee
Truncated 6-demicube	thax
Runcic 6-cube	sirhax
Steric 6-cube	sophax
Pentic 6-cube	sochax
Rectified 6-cube	rax
Tritruncated 6-cube	xog
Bicantellated 6-orthoplex	siborg
Runcinated 6-orthoplex	spog
Bitruncated 6-orthoplex	botag
Cantellated 6-orthoplex	srog
Truncated 6-orthoplex	tag
Runcicantic 6-cube	girhax
Stericantic 6-cube	pithax
Penticantic 6-cube	cathix
Bitruncated 6-cube	botox
Steriruncic 6-cube	prohax
Pentiruncic 6-cube	crohax
Bicantellated 6-cube	saborx
Pentisteric 6-cube	cophix
Biruncinated 6-cube	sobpoxog
Stericated 6-orthoplex	scag
Bicantitruncated 6-orthoplex	gaborg
Runcicantellated 6-orthoplex	prog
Runcitruncated 6-orthoplex	potag
Cantitruncated 6-orthoplex	grog
Steriruncicantic 6-cube	gophax
Pentiruncicantic 6-cube	cagrohax
Bicantitruncated 6-cube	gaborx
Pentistericantic 6-cube	capthix
Biruncitruncated 6-cube	boprag
Steriruncinated 6-orthoplex	copog
Pentisteriruncic 6-cube	caprohax
Biruncitruncated 6-orthoplex	boprax
Stericantellated 6-orthoplex	crag
Steritruncated 6-orthoplex	catog
Runcicantitruncated 6-orthoplex	gopog
Pentisteriruncicantic 6-cube	gochax
Biruncicantitruncated 6-cube	gobpoxog
Steriruncicantellated 6-orthoplex	coprag
Steriruncitruncated 6-orthoplex	captog
Stericantitruncated 6-orthoplex	cagorg
Steriruncicantitruncated 6-orthoplex	gocog

Runcicantitruncated 6-orthoplex

Contents

Vertex coordinates[edit | edit source]

Representations[edit | edit source]

Gallery[edit | edit source]

External links[edit | edit source]

Navigation menu

Runcicantitruncated 6-orthoplex

Vertex coordinates[edit | edit source]

Representations[edit | edit source]

Gallery[edit | edit source]

External links[edit | edit source]

Navigation menu

Search