Torus (EntityTopic, 11)
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- | {{Shape|Torus|http://img56.imageshack.us/img56/5955/torus0oy.png|3|1, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]]Q|(21) ((x,y),z)|N/A|N/A|N/A}} | + | {{Shape|Torus|http://img56.imageshack.us/img56/5955/torus0oy.png|3|1, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]]Q|(21) ((x,y),z)|N/A|N/A|N/A|13}} |
== Geometry == | == 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'''. | 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'''. | ||
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*The [[planar]] [[cross-section]]s (''n'') of a torus are: | *The [[planar]] [[cross-section]]s (''n'') of a torus are: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
- | + | ||
{{Polyhedra}} | {{Polyhedra}} | ||
- | {{ | + | {{Rotope Nav|12|13|14|(II)'<br>Cone|((II)I)<br>Torus|IIII<br>Tesseract}} |
Revision as of 12:17, 17 June 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
- Assumption: Torus is centered at the origin, with the base in the xy plane.
- 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 |