Cone (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape| | + | {{STS Shape |
| + | | image=http://img137.imageshack.us/img137/6835/cone1er.png | ||
| + | | dim=3 | ||
| + | | elements=2, 1, 1 | ||
| + | | genus=0 | ||
| + | | ssc=(xy)P | ||
| + | | extra={{STS Rotope | ||
| + | | attrib=pure | ||
| + | | notation=2<sup>1</sup> | ||
| + | | index=12 | ||
| + | }}{{STS Uniform polytope | ||
| + | | vfigure=[[Circle]], radius 1 | ||
| + | }}}} | ||
| + | |||
A '''cone''' is a special case of a [[pyramid]] where the base is a [[circle]]. | A '''cone''' is a special case of a [[pyramid]] where the base is a [[circle]]. | ||
Revision as of 15:50, 14 March 2008
A cone is a special case of a pyramid where the base is a circle.
The cone is one of the few curved polyhedra that satisfy Euler's F + V = E + 2.
Equations
- Variables:
r ⇒ radius of base of cone
h ⇒ height of cone
- All points (x, y, z) that lie on the surface of a cone will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the edges of a cone will satisfy the following equations:
x2 + y2 = r2
z = 0
- The hypervolumes of a cone are given by:
total edge length = 2πr
surface area = πr2 + πrsqrt(h2 + r2)
volume = πr2h3-1
- The planar cross-sections (n) of a cone are:
[!x,!y] ⇒ Unknown
[!z] ⇒ circle of radius (r-rnh-1)
| 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 |
