Square gyrobicupolic ring (EntityTopic, 17)

From Higher Dimensions Database


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-√22),√(√22));
(±√2,0,√(2-√22),-√(√22));
(0,±√2,√(2-√22),-√(√22)).

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) · l2
surcell volume = Unknown
bulk = Unknown
[!x,!y] ⇒ Unknown
[!z] ⇒ Unknown
[!w] ⇒ Unknown

Software models


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonediconeconinder
Torii: tigertorispherespheritorustorinderditorus