Square orthobicupolic ring (EntityTopic, 17)

From Higher Dimensions Database


The square orthobicupolic 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 cube, and then filling in the gaps with 4 triangular prisms and 4 tetrahedra. For faces, it contains one octagon, 14 squares and 16 triangles.

Cartesian coordinates

The coordinates of the square orthobicupolic ring are as follows:

(±(1+√2),±1,0,0);
(±1,±(1+√2),0,0);
(±1,±1,1,±1).

Equations

  • Variables:
l ⇒ edge length
  • The hypervolumes of a square orthobicupolic ring are given by:
total edge length = 36l
total surface area = 2(8 + √2 + 2√3) · l2
surcell volume = Unknown
bulk = Unknown
[!x,!y] ⇒ Unknown
[!z] ⇒ Unknown
[!w] ⇒ Unknown


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