In six-dimensional geometry, a **cantellated 5-cube** is a convex uniform 5-polytope, being a cantellation of the regular 5-cube.

There are 6 unique cantellation for the 5-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex

Small rhombated penteract (Acronym: sirn) (Jonathan Bowers)
The Cartesian coordinates of the vertices of a *cantellated 5-cube* having edge length 2 are all permutations of:

(
±
1
,
±
1
,
±
(
1
+
2
)
,
±
(
1
+
2
)
,
±
(
1
+
2
)
)
In five-dimensional geometry, a **bicantellated 5-cube** is a uniform 5-polytope.

Bicantellated penteract, bicantellated 5-orthoplex, or bicantellated pentacross
Small birhombated penteractitriacontiditeron (Acronym: sibrant) (Jonathan Bowers)
The Cartesian coordinates of the vertices of a *bicantellated 5-cube* having edge length 2 are all permutations of:

(0,1,1,2,2)

Tricantitruncated 5-orthoplex / tricantitruncated pentacross
Great rhombated penteract (girn) (Jonathan Bowers)
The Cartesian coordinates of the vertices of an cantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

(
1
,
1
+
2
,
1
+
2
2
,
1
+
2
2
,
1
+
2
2
)
Bicantitruncated penteract
Bicantitruncated pentacross
Great birhombated penteractitriacontiditeron (Acronym: gibrant) (Jonathan Bowers)

Cartesian coordinates for the vertices of a bicantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of

(±3,±3,±2,±1,0)

These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.