Stericated 7-cubes

In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.

Orthogonal projections in B6 Coxeter plane
7-cube	Stericated 7-cube	Bistericated 7-cube
Steritruncated 7-cube	Bisteritruncated 7-cube	Stericantellated 7-cube
Bistericantellated 7-cube	Stericantitruncated 7-cube	Bistericantitruncated 7-cube
Steriruncinated 7-cube	Steriruncitruncated 7-cube	Steriruncicantellated 7-cube
Bisteriruncitruncated 7-cube	Steriruncicantitruncated 7-cube	Bisteriruncicantitruncated 7-cube

There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex.

This polytope is one of 127 uniform 7-polytopes with B₇ symmetry.

Stericated 7-cube

Stericated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Small cellated hepteract (acronym: ) (Jonathan Bowers)^[1]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Bistericated 7-cube

bistericated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)^[2]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Steritruncated 7-cube

steritruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,1,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Cellitruncated hepteract (acronym: ) (Jonathan Bowers)^[3]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Bisteritruncated 7-cube

bisteritruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,2,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)^[4]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Stericantellated 7-cube

Stericantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Cellirhombated hepteract (acronym: ) (Jonathan Bowers)^[5]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Bistericantellated 7-cube

Bistericantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Bicellirhombihepteract (acronym: ) (Jonathan Bowers)^[6]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Stericantitruncated 7-cube

stericantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,1,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)^[7]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Bistericantitruncated 7-cube

bistericantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,2,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)^[8]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Steriruncinated 7-cube

Steriruncinated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Celliprismated hepteract (acronym: ) (Jonathan Bowers)^[9]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Steriruncitruncated 7-cube

steriruncitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,1,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)^[10]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Steriruncicantellated 7-cube

steriruncicantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)^[11]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Bisteriruncitruncated 7-cube

bisteriruncitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,2,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)^[12]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]

Steriruncicantitruncated 7-cube

steriruncicantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t0,1,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Great cellated hepteract (acronym: ) (Jonathan Bowers)^[13]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph	too complex	too complex
Dihedral symmetry	[6]	[4]

Bisteriruncicantitruncated 7-cube

bisteriruncicantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t1,2,3,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,35]
Properties	convex

Alternate names

• Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers) ^[14]

Images

orthographic projections

Coxeter plane	B7 / A6	B6 / D7	B5 / D6 / A4
Graph	too complex
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B4 / D5	B3 / D4 / A2	B2 / D3
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A5	A3
Graph
Dihedral symmetry	[6]	[4]