Ditorus (EntityTopic, 11)
From Hi.gher. Space
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*All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a ditorus will satisfy the following equation: | *All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a ditorus will satisfy the following equation: | ||
| - | <blockquote> | + | <blockquote>(√((√(''x''<sup>2</sup> + ''y''<sup>2</sup>) − ''ρ'')<sup>2</sup> + ''z''<sup>2</sup>) − ''r'')<sup>2</sup> + ''w''<sup>2</sup> = ''R''<sup>2</sup></blockquote> |
| - | (√((√(''x''<sup>2</sup> + ''y''<sup>2</sup>) | + | |
| - | </blockquote> | + | |
*The parametric equations are: | *The parametric equations are: | ||
Revision as of 10:29, 12 March 2011
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 th3) cos th2) cos th1
y = (R + (r + ρ cos th3) cos th2) sin th1
z = (r + ρ cos th3) sin th2
w = a sin th3
- 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
| 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 | |||||
