Pentic 6-cubes

In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.

There are 8 pentic forms of the 6-cube.

Pentic 6-cube
The pentic 6-cube,, has half of the vertices of a pentellated 6-cube,.

Alternate names

 * Stericated 6-demicube/demihexeract
 * Small cellated hemihexeract (Acronym: sochax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±1,±1,±1,±3)

with an odd number of plus signs.

Penticantic 6-cube
The penticantic 6-cube,, has half of the vertices of a penticantellated 6-cube,.

Alternate names

 * Steritruncated 6-demicube/demihexeract
 * cellitruncated hemihexeract (Acronym: cathix) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±3,±3,±3,±5)

with an odd number of plus signs.

Pentiruncic 6-cube
The pentiruncic 6-cube,, has half of the vertices of a pentiruncinated 6-cube (penticantellated 6-orthoplex),.

Alternate names

 * Stericantellated 6-demicube/demihexeract
 * cellirhombated hemihexeract (Acronym: crohax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±1,±3,±3,±5)

with an odd number of plus signs.

Pentiruncicantic 6-cube
The pentiruncicantic 6-cube,, has half of the vertices of a pentiruncicantellated 6-cube or (pentiruncicantellated 6-orthoplex),

Alternate names

 * Stericantitruncated demihexeract, stericantitruncated 7-demicube
 * Great cellated hemihexeract (Acronym: cagrohax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

Pentisteric 6-cube
The pentisteric 6-cube,, has half of the vertices of a pentistericated 6-cube (pentitruncated 6-orthoplex),

Alternate names

 * Steriruncinated 6-demicube/demihexeract
 * Small cellipriamated hemihexeract (Acronym: cophix) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±1,±1,±3,±5)

with an odd number of plus signs.

Pentistericantic 6-cube
The pentistericantic 6-cube,, has half of the vertices of a pentistericantellated 6-cube (pentiruncitruncated 6-orthoplex),.

Alternate names

 * Steriruncitruncated demihexeract/7-demicube
 * cellitruncated hemihexeract (Acronym: capthix) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

Pentisteriruncic 6-cube
The pentisteriruncic 6-cube,, has half of the vertices of a pentisteriruncinated 6-cube (penticantitruncated 6-orthoplex),.

Alternate names

 * Steriruncicantellated 6-demicube/demihexeract
 * Celliprismatorhombated hemihexeract (Acronym: caprohax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±1,±3,±5,±7)

with an odd number of plus signs.

Pentisteriruncicantic 6-cube
The pentisteriruncicantic 6-cube,, has half of the vertices of a pentisteriruncicantellated 6-cube (pentisteriruncicantitruncated 6-orthoplex),.

Alternate names

 * Steriruncicantitruncated 6-demicube/demihexeract
 * Great cellated hemihexeract (Acronym: gochax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
 * (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

Related polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: