Ditorus (EntityTopic, 11)
From Hi.gher. Space
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*The [[realmic]] [[cross-section]]s (''n'') of a ditorus are: | *The [[realmic]] [[cross-section]]s (''n'') of a ditorus are: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
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| + | == Cross-sections == | ||
| + | [[User:Polyhedron Dude|Jonathan Bowers aka Polyhedron Dude]] created these two excellent cross-section renderings: | ||
| + | <[#img [hash H6DXEQ7GQ5WXY6TJR4JYWJVEZA] [width 933] [height 279]]> | ||
| + | <[#img [hash GGJMWW6SCSZ8ESAMECBKYNZAXP] [width 1105] [height 293]]> | ||
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{{Tetrashapes}} | {{Tetrashapes}} | ||
{{Toratope Nav B|7|8|9|(III)I<br>Spherinder|((III)I)<br>Toraspherinder|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|chora}} | {{Toratope Nav B|7|8|9|(III)I<br>Spherinder|((III)I)<br>Toraspherinder|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|chora}} | ||
Revision as of 21:05, 10 December 2013
The ditorus is a four-dimensional torus formed by taking an uncapped torinder and connecting its ends either in a loop or through its inside. Its toratopic dual is itself.
Equations
- Variables:
R ⇒ major-major radius of the ditorus
r ⇒ major-minor radius of the ditorus
ρ ⇒ minor-minor radius of the ditorus
- All points (x, y, z, w) that lie on the surcell of a ditorus will satisfy the following equation:
(√((√(x2 + y2) − ρ)2 + z2) − r)2 + w2 = R2
- The parametric equations are:
x = (R + (r + ρ cos θ3) cos θ2) cos θ1
y = (R + (r + ρ cos θ3) cos θ2) sin θ1
z = (r + ρ cos θ3) sin θ2
w = a sin θ3
- The hypervolumes of a ditorus are given by:
total surface area = 0
surcell volume = 8π3Rrρ
bulk = 4π3ρ2rR
- The realmic cross-sections (n) of a ditorus are:
Unknown
Cross-sections
Jonathan Bowers aka Polyhedron Dude created these two excellent cross-section renderings: ExPar: [#img] is obsolete, use [#embed] instead ExPar: [#img] is obsolete, use [#embed] instead
| 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 |
| 7a. (III)I Spherinder | 7b. ((III)I) Toraspherinder | 8a. ((II)I)I Torinder | 8b. (((II)I)I) Ditorus | 9a. IIIII Penteract | 9b. (IIIII) Pentasphere |
| List of toratopes | |||||
