Torus (EntityTopic, 11)
From Hi.gher. Space
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Revision as of 20:14, 17 August 2007
Geometry
A torus is a special case of a surface of revolution where the base is a circle. The circle's radius is known as the minor radius and the distance from the center of the circle to the center of the torus is known as the major radius.
Equations
- Variables:
R ⇒ major radius of torus
r ⇒ minor radius of torus
- All points (x, y, z) that lie on the surface of a torus will satisfy the following equation:
(R-sqrt(x2+y2))2 + z2 = r2
- The hypervolumes of a torus are given by:
total edge length = 0
surface area = 4π2Rr
volume = 2π2Rr2
- The planar cross-sections (n) of a torus are:
Unknown
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
