Torisphere (EntityTopic, 11)
From Hi.gher. Space
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m (moved Toraspherinder to Torisphere: toraspherinder -> torisphere) |
Revision as of 19:10, 2 February 2014
The toraspherinder is a four-dimensional torus formed by taking an uncapped spherinder and connecting its ends through its inside. Its toratopic dual is the toracubinder.
Equations
- Variables:
r ⇒ minor radius of the toraspherinder
R ⇒ major radius of the toraspherinder
- All points (x, y, z, w) that lie on the surcell of a toraspherinder will satisfy the following equation:
(√(x2 + y2 + z2) − R)2 + w2 = r2
- The parametric equations are:
x = r cos a cos b cos c + R cos b cos c
y = r cos a cos b sin c + R cos b sin c
z = r cos a sin b + R sin b
w = r sin a
- The hypervolumes of a toraspherinder are given by:
total edge length = 0
total surface area = 0
surcell volume = 8π2Rr2
bulk = 8π2Rr33-1
- The realmic cross-sections (n) of a toraspherinder 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 |
6a. (II)(II) Duocylinder | 6b. ((II)(II)) Tiger | 7a. (III)I Spherinder | 7b. ((III)I) Toraspherinder | 8a. ((II)I)I Torinder | 8b. (((II)I)I) Ditorus |
List of toratopes |