# CRFP4DP/Gyrations (Meta, 14)

### From Hi.gher. Space

wintersolstice discovered that some CRFs can be gyrated in various ways. For example, a cube||rhombicuboctahedron can have a square orthobicupolic ring cut off and replaced with a square gyrobicupolic ring.

The cantellated tesseract is a rich source of CRFs obtained by cutting off square magnabicupolic rings and gluing them back on with the "wrong" orientation (i.e., with the octagonal prism base rotated 45°). As a result, some octahedral cells are cut into square pyramids, and some rhombicuboctahedral cells are gyrated into pseudo-rhombicuboctahedra (elongated square gyrobicupola). Among the possibilies are:

- Paratetragyrated cantellated tesseract: 4 antipodal square magnabicupolic rings lying on two orthogonal great circles are gyrated, producing a polychoron with 8 pseudo-rhombicuboctahedra, and a number of square pyramids that meet with triangular prisms in an irregular way.

- Orthotetragyrated cantellated tesseract: 4 square magnabicupolic rings lying on the same great circle are gyrated. The result is a modified cantellated tesseract where 4 of the rhombicuboctahedral cells are "aligned wrongly" with the other 4.
- Octagyrated cantellated tesseract: discovered by Dr. Klitzing in January 2013, this polychoron consists of 8 rhombicuboctahedra, 32 square pyramids, and 32 triangular prisms.
- Two magnabicupolic rings lying on opposite ends of a single rhombicuboctahedron can be removed, and then one of them glued back onto the octagonal prism that remains from the original rhombicuboctahedral cell. This produces a fastigium-like CRF with 5-fold loop around one great circle (4 elongated square cupola + 1 rhombicuboctahedron), an odd deviation from tesseractic symmetry.
- The full set of possibilities has yet to be enumerated.