Pentic 7-cubes

In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms.

More information Orthogonal projections in D7 Coxeter plane ...

Orthogonal projections in D₇ Coxeter plane
7-demicube (half 7-cube, h{4,3⁵})	Pentic 7-cube h₅{4,3⁵}	Penticantic 7-cube h_2,5{4,3⁵}
Pentiruncic 7-cube h_3,5{4,3⁵}	Pentiruncicantic 7-cube h_2,3,5{4,3⁵}	Pentisteric 7-cube h_4,5{4,3⁵}
Pentistericantic 7-cube h_2,4,5{4,3⁵}	Pentisteriruncic 7-cube h_3,4,5{4,3⁵}	Penticsteriruncicantic 7-cube h_2,3,4,5{4,3⁵}

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Coxeter plane	B₇	D₇	D₆
Graph
Dihedral symmetry	[14/2]	[12]	[10]
Coxeter plane	D₅	D₄	D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Dimensional family of pentic n-cubes
n	6	7	8
[1⁺,4,3^n-2] = [3,3^n-3,1]	[1⁺,4,3⁴] = [3,3^3,1]	[1⁺,4,3⁵] = [3,3^4,1]	[1⁺,4,3⁶] = [3,3^5,1]
Cantic figure
Coxeter	=	=	=
Schläfli	h₅{4,3⁴}	h₅{4,3⁵}	h₅{4,3⁶}

Coxeter plane	B₇	D₇	D₆
Graph
Dihedral symmetry	[14/2]	[12]	[10]
Coxeter plane	D₅	D₄	D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Coxeter plane	B₇	D₇	D₆
Graph
Dihedral symmetry	[14/2]	[12]	[10]
Coxeter plane	D₅	D₄	D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Pentic 7-cube

v t e Fundamental convex regular and uniform polytopes in dimensions 2–10
Family	$A n$	$B n$	$I 2 (p)$ / $D n$	$E 6$ / $E 7$ / $E 8$ / $F 4$ / $G 2$	$H n$
Regular polygon	Triangle	Square	p-gon	Hexagon	Pentagon
Uniform polyhedron	Tetrahedron	Octahedron • Cube	Demicube		Dodecahedron • Icosahedron
Uniform polychoron	Pentachoron	16-cell • Tesseract	Demitesseract	24-cell	120-cell • 600-cell
Uniform 5-polytope	5-simplex	5-orthoplex • 5-cube	5-demicube
Uniform 6-polytope	6-simplex	6-orthoplex • 6-cube	6-demicube	1₂₂ • 2₂₁
Uniform 7-polytope	7-simplex	7-orthoplex • 7-cube	7-demicube	1₃₂ • 2₃₁ • 3₂₁
Uniform 8-polytope	8-simplex	8-orthoplex • 8-cube	8-demicube	1₄₂ • 2₄₁ • 4₂₁
Uniform 9-polytope	9-simplex	9-orthoplex • 9-cube	9-demicube
Uniform 10-polytope	10-simplex	10-orthoplex • 10-cube	10-demicube
Uniform n-polytope	n-simplex	n-orthoplex • n-cube	n-demicube	1_k2 • 2_k1 • k₂₁	n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds • Polytope operations