# Square gyrobicupolic ring (EntityTopic, 17)

### From Hi.gher. Space

The **square gyrobicupolic ring** is a CRF polychoron discovered by Keiji. It is a member of the family of bicupolic rings, which contains eight other similar polychora. It is formed by attaching two square cupolae by their octagonal faces, folding them into the fourth dimension with their square ends connected by a square antiprism, and then filling in the gaps with 8 square pyramids. For faces, it contains one octagon, 10 squares and 24 triangles.

## Cartesian coordinates

The coordinates of the square gyrobicupolic ring are as follows:

(±(1+√2),±1,0,0);

(±1,±(1+√2),0,0);

(±1,±1,√(2-^{√2}∕_{2}),√(^{√2}∕_{2}));

(±√2,0,√(2-^{√2}∕_{2}),-√(^{√2}∕_{2}));

(0,±√2,√(2-^{√2}∕_{2}),-√(^{√2}∕_{2})).

## Equations

- Variables:

l⇒ edge length

- The hypervolumes of a square gyrobicupolic ring are given by:

total edge length = 40l

total surface area = 2(6 + √2 + 3√3) ·l^{2}

surcell volume =Unknown

bulk =Unknown

- The realmic cross-sections (
*n*) of a square gyrobicupolic ring are:

[!x,!y] ⇒Unknown

[!z] ⇒Unknown

[!w] ⇒Unknown

## Software models

Notable Tetrashapes
| |

Regular:
| pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |

Powertopes:
| triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |

Circular:
| glome • cubinder • duocylinder • spherinder • sphone • dicone • coninder |

Torii:
| tiger • torisphere • spheritorus • torinder • ditorus |