Pentic 6 cubes

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 of a pentic 6-cube 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 of a stericantitruncated demihexeract 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 of a pentiruncic 6-cube 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 of a pentiruncicantic 6-cube 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 of a pentisteric 6-cube 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

Steriruncicantitruncated demihexeract/7-demicube

cellitruncated hemihexeract (Acronym: capthix) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the vertices of a pentistericantic 6-cube 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 of a pentisteriruncic 6-cube 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 of a pentisteriruncicantic 6-cube 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 BC₆ symmetry, and 16 are unique: