Torinder (EntityTopic, 11)
From Hi.gher. Space
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{{Shape|Torinder|''No image''|4|?, ?, ?, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Torus|Q]]E|(21)1 ((x,y),z),w|N/A|N/A|N/A|40|N/A|N/A|pure}} | {{Shape|Torinder|''No image''|4|?, ?, ?, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Torus|Q]]E|(21)1 ((x,y),z),w|N/A|N/A|N/A|40|N/A|N/A|pure}} | ||
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A '''torinder''' is the linear extension of a [[torus]]. | A '''torinder''' is the linear extension of a [[torus]]. | ||
- | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''R'' ⇒ major radius of the torinder<br> | <blockquote>''R'' ⇒ major radius of the torinder<br> |
Revision as of 20:23, 22 September 2007
Template:Shape 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 |