Torisphere (EntityTopic, 11)
From Hi.gher. Space
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| ssc=[(xyz)w]T | | ssc=[(xyz)w]T | ||
| ssc2=T((3)1) | | ssc2=T((3)1) | ||
| - | | extra={{STS | + | | extra={{STS Toratope |
| - | | | + | | holeseq=[1, 1] |
| - | | notation= | + | | notation=((III)I) |
| - | | index= | + | | index=7b |
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{{Tetrashapes}} | {{Tetrashapes}} | ||
| - | {{ | + | {{Toratope Nav B|6|7|8|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|(III)I<br>Spherinder|((III)I)<br>Toraspherinder|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|chora}} |
Revision as of 20:46, 24 November 2009
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 |
| 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 | |||||
