Cone (EntityTopic, 11)
From Hi.gher. Space
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Revision as of 18:28, 24 November 2009
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)
Arrinder
An arrinder is the surface of revolution of an arrow, just as a cone is the surface of revolution of a triangle. It can also be thought of as a cone with a smaller cone removed from the base. As such, this shape's volume is the difference between the volume of the two aforementioned cones.
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 |
7. 111 Cube | 8. 21 Cone | 9. [11]1 |
List of tapertopes |