Square orthobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
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The '''square orthobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[square cupola]]e by their [[octagon]]al faces, folding them into the fourth dimension with their [[square]] ends connected by a [[cube]], and then filling in the gaps with 4 [[triangular prism]]s and 4 [[tetrahedra]]. For faces, it contains one octagon, 14 squares and 16 [[triangle]]s. | The '''square orthobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[square cupola]]e by their [[octagon]]al faces, folding them into the fourth dimension with their [[square]] ends connected by a [[cube]], and then filling in the gaps with 4 [[triangular prism]]s and 4 [[tetrahedra]]. For faces, it contains one octagon, 14 squares and 16 [[triangle]]s. | ||
| + | |||
| + | == Cartesian coordinates == | ||
| + | The coordinates of the square orthobicupolic ring are as follows: | ||
| + | <blockquote> | ||
| + | (±(1+√2),±1,0,0);<br /> | ||
| + | (±1,±(1+√2),0,0);<br /> | ||
| + | (±1,±1,1,±1). | ||
| + | </blockquote> | ||
== Equations == | == Equations == | ||
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[!z] ⇒ ''Unknown''<br /> | [!z] ⇒ ''Unknown''<br /> | ||
[!w] ⇒ ''Unknown''</blockquote> | [!w] ⇒ ''Unknown''</blockquote> | ||
| + | |||
| + | ==Software models== | ||
| + | |||
| + | *[[Polyview]] [http://hddb.teamikaria.com/dl/ZZ3QPX5HWXQD2X0B2XPDGG3PVN.def .def file] | ||
| + | *[[Stella4D]] [http://hddb.teamikaria.com/dl/QSCXGC36CW4KPKZ755ZS6APHT4.off .off file] | ||
{{Clear}} | {{Clear}} | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
Latest revision as of 23:06, 23 May 2014
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
- The realmic cross-sections (n) of a square orthobicupolic 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 • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
