Torinder (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
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| name=Torinder | | name=Torinder | ||
| dim=4 | | dim=4 | ||
| elements=?, ?, ?, 0 | | elements=?, ?, ?, 0 | ||
| genus=1 | | genus=1 | ||
| - | |||
| ssc=[x[(yz)w]T] | | ssc=[x[(yz)w]T] | ||
| - | | | + | | extra={{STS Rotope |
| - | | | + | | attrib=pure |
| - | }} | + | | notation=(21)1 ((x,y),z),w |
| + | | index=40 | ||
| + | }}}} | ||
A '''torinder''' is the linear extension of a [[torus]]. | A '''torinder''' is the linear extension of a [[torus]]. | ||
Revision as of 15:34, 14 March 2008
A torinder is the linear extension of a torus.
Equations
- Variables:
R ⇒ major radius of the torinder
r ⇒ minor radius of the torinder
h ⇒ height of the torinder
- All points (x, y, z, w) that lie on the surcell of a torinder will satisfy the following equation:
h ≥ |w|
r2 = (sqrt(x2 + y2) - R)2 + z2
- The parametric equations are:
x = (R + r cos(θ)) cos(Φ)
y = (R + r cos(θ)) sin(Φ)
z = r sin(θ)
w = w
- The hypervolumes of a torinder are given by:
surface area of margin = 8π2Rr
surcell volume = 4πRr(πr + h)
bulk = 2π2Rr2h
- The realmic cross-sections (n) of a torinder 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 |
