Stericated 5-cubes

• Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
• Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
• Small cellated penteractitriacontaditeron (Acronym: scant) (Jonathan Bowers)[1]

The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:

${\displaystyle \left(\pm 1,\ \pm 1,\ \pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}})\right)}$

The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

orthographic projections

Coxeter plane	B5	B4 / D5	B3 / D4 / A2
Graph
Dihedral symmetry	[10]	[8]	[6]
Coxeter plane	B2	A3
Graph
Dihedral symmetry	[4]	[4]

• Steritruncated penteract
• Celliprismated triacontaditeron (Acronym: capt) (Jonathan Bowers)[2]

The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:

${\displaystyle \left(\pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+2{\sqrt {2}})\right)}$

• Stericantellated penteract
• Stericantellated 5-orthoplex, stericantellated pentacross
• Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)[3]

The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:

${\displaystyle \left(\pm 1,\ \pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+2{\sqrt {2}})\right)}$

• Stericantitruncated penteract
• Steriruncicantellated triacontiditeron / Biruncicantitruncated pentacross
• Celligreatorhombated penteract (cogrin) (Jonathan Bowers)[4]

The Cartesian coordinates of the vertices of an stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

${\displaystyle \left(1,\ 1+{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+3{\sqrt {2}}\right)}$

• Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
• Celliprismatotruncated penteractitriacontiditeron (captint) (Jonathan Bowers)[5]

The Cartesian coordinates of the vertices of an steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

${\displaystyle \left(1,\ 1+{\sqrt {2}},\ 1+1{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+3{\sqrt {2}}\right)}$

• Steritruncated pentacross
• Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)[6]

Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

${\displaystyle \left(\pm 1,\ \pm 1,\ \pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}})\right)}$

• Stericantitruncated pentacross
• Celligreatorhombated triacontaditeron (cogart) (Jonathan Bowers)[7]

The Cartesian coordinates of the vertices of an stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:

${\displaystyle \left(1,\ 1,\ 1+{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+3{\sqrt {2}}\right)}$

• Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson)
• Omnitruncated penteract
• Omnitruncated triacontiditeron / omnitruncated pentacross
• Great cellated penteractitriacontiditeron (Jonathan Bowers)[8]

The Cartesian coordinates of the vertices of an omnitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

${\displaystyle \left(1,\ 1+{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+3{\sqrt {2}},\ 1+4{\sqrt {2}}\right)}$

The full snub 5-cube or omnisnub 5-cube, defined as an alternation of the omnitruncated 5-cube is not uniform, but it can be given Coxeter diagram and symmetry [4,3,3,3]⁺, and constructed from 10 snub tesseracts, 32 snub 5-cells, 40 snub cubic antiprisms, 80 snub tetrahedral antiprisms, 80 3-4 duoantiprisms, and 1920 irregular 5-cells filling the gaps at the deleted vertices.