Torisphere (EntityTopic, 11)
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{{Shape|Toraspherinder|''No image''|4|1, 0, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]Q|(31) ((x,y,z),w)|N/A|N/A|N/A|22|N/A|N/A|pure}} | {{Shape|Toraspherinder|''No image''|4|1, 0, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]Q|(31) ((x,y,z),w)|N/A|N/A|N/A|22|N/A|N/A|pure}} | ||
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The toraspherinder is a special case of a [[surcell of revolution]] where the base is a [[sphere]]. | The toraspherinder is a special case of a [[surcell of revolution]] where the base is a [[sphere]]. | ||
| - | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''r'' ⇒ minor radius of the toraspherinder <br> | <blockquote>''r'' ⇒ minor radius of the toraspherinder <br> | ||
Revision as of 20:20, 22 September 2007
Template:Shape 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 |
