Square gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
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- | <[#ontology [kind topic] [cats | + | <[#ontology [kind topic] [cats Bicupolic_ring]]> |
{{STS Shape | {{STS Shape | ||
- | | image=<[# | + | | image=<[#embed [hash 84ZQE0313240PWV0MBZWTCYHRV] [width 180]]> |
| dim=4 | | dim=4 | ||
| elements=11, 35, 40, 16 | | elements=11, 35, 40, 16 | ||
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The '''square gyrobicupolic 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 [[square antiprism]], and then filling in the gaps with 8 [[square pyramid]]s. For faces, it contains one octagon, 10 squares and 24 [[triangle]]s. | The '''square gyrobicupolic 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 [[square antiprism]], and then filling in the gaps with 8 [[square pyramid]]s. For faces, it contains one octagon, 10 squares and 24 [[triangle]]s. | ||
+ | |||
+ | == Cartesian coordinates == | ||
+ | The coordinates of the square gyrobicupolic ring are as follows: | ||
+ | <blockquote> | ||
+ | (±(1+√2),±1,0,0);<br /> | ||
+ | (±1,±(1+√2),0,0);<br /> | ||
+ | (±1,±1,√(2-{{Over|√2|2}}),√({{Over|√2|2}}));<br /> | ||
+ | (±√2,0,√(2-{{Over|√2|2}}),-√({{Over|√2|2}}));<br /> | ||
+ | (0,±√2,√(2-{{Over|√2|2}}),-√({{Over|√2|2}})). | ||
+ | </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/MT1SW1SGTAA92P0SYDXVETB9ZP.def .def file] | ||
+ | *[[Stella4D]] [http://hddb.teamikaria.com/dl/E32MAFTZAF0NP4SSS6TXTP6XGW.off .off file] | ||
{{Clear}} | {{Clear}} | ||
{{Tetrashapes}} | {{Tetrashapes}} |
Latest revision as of 23:09, 23 May 2014
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) · l2
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 • cylindrone • dicone • coninder |
Torii: | tiger • torisphere • spheritorus • torinder • ditorus |