Cone (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape|Cone|http://img137.imageshack.us/img137/6835/cone1er.png|3|2, 1, 1|0|N/A|N/A|[[Line (object)|E]][[Circle|L]]T|2<sup>1</sup>|[[Circle]], radius 1|N/A|N/A}} | + | {{Shape|Cone|http://img137.imageshack.us/img137/6835/cone1er.png|3|2, 1, 1|0|N/A|N/A|[[Line (object)|E]][[Circle|L]]T|2<sup>1</sup>|[[Circle]], radius 1|N/A|N/A|12}} |
== Geometry == | == Geometry == | ||
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]]. | ||
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<br clear="all"><br> | <br clear="all"><br> | ||
{{Polyhedra}} | {{Polyhedra}} | ||
| - | {{ | + | {{Rotope Nav|11|12|13|(II)I<br>Cylinder|(II)'<br>Cone|((II)I)<br>Torus}} |
Revision as of 12:15, 17 June 2007
Geometry
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
- Assumption: Cone's base is centered at the origin.
- 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 |
