Torisphere (EntityTopic, 11)
From Hi.gher. Space
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Revision as of 20:19, 17 August 2007
Geometry
The toraspherinder is a special case of a surcell of revolution where the base is a sphere.
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:(?)
(sqrt(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 |
