Spheritorus (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
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| name=Toracubinder | | name=Toracubinder | ||
| dim=4 | | dim=4 | ||
| elements=1, ?, ?, 0 | | elements=1, ?, ?, 0 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=[xyz], [x<sup>3</sup>] or {G4<sup>3</sup>} | | ssc=[xyz], [x<sup>3</sup>] or {G4<sup>3</sup>} | ||
| - | | | + | | extra={{STS Rotope |
| - | | | + | | attrib=pure |
| - | + | | notation=(211) ((x,y),z,w) | |
| - | }} | + | | index=36 |
| + | }}}} | ||
The '''toracubinder''' is a special case of a [[surcell of revolution]] where the base is a [[cylinder]]. | The '''toracubinder''' is a special case of a [[surcell of revolution]] where the base is a [[cylinder]]. | ||
Revision as of 15:36, 14 March 2008
The toracubinder is a special case of a surcell of revolution where the base is a cylinder.
Equations
- Variables:
R ⇒ major radius of the toracubinder
r ⇒ minor radius of the toracubinder
h ⇒ height of the toracubinder
- All points (x, y, z, w) that lie on the surcell of a toracubinder will satisfy the following equation:
(sqrt(x2+y2)-R)2 + z2 + w2 = r2
- The parametric equations are:
x = r cos a cos b cos c + R cos c
y = r cos a cos b sin c + R sin c
z = r cos a sin b
w = r sin a
- The hypervolumes of a toracubinder are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = 4π2Rr(r+h)
bulk = 2π2Rr2h
- The realmic cross-sections (n) of a toracubinder 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 |
