Dicone (EntityTopic, 11)
From Hi.gher. Space
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| - | A '''dicone''' is a special case of a [[pyramid]] where the base is a [[cone]]. It is also a special case of a [[dipyramid]] where the base is a [[circle]]. | + | A '''dicone''' is a special case of a [[pyramid]] where the base is a [[cone]]. It is also a special case of a [[dipyramid]] where the base is a [[circle]]. It is bounded by two cones and a triangular torus made by rotating a triangle around one edge while the opposite vertex traces out a circle lying in a plane parallel from the edge. |
== Equations == | == Equations == | ||
Revision as of 06:25, 3 September 2008
A dicone is a special case of a pyramid where the base is a cone. It is also a special case of a dipyramid where the base is a circle. It is bounded by two cones and a triangular torus made by rotating a triangle around one edge while the opposite vertex traces out a circle lying in a plane parallel from the edge.
Equations
- Variables:
r ⇒ radius of base of dicone
h ⇒ height of dicone
- All points (x, y, z, w) that lie on the surface of a dicone will satisfy the following equations:
Unknown
- The hypervolumes of a dicone are given by:
Unknown
- The realmic cross-sections (n) of a dicone are:
Unknown
Projection
The following are the two possible types of parallel projections for a dicone:
http://fusion-global.org/share/dicone.png
The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.
| 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 |
