Cone (EntityTopic, 11)
From Hi.gher. Space
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<blockquote>[!x,!y] ⇒ ''Unknown''<br> | <blockquote>[!x,!y] ⇒ ''Unknown''<br> | ||
[!z] ⇒ circle of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | [!z] ⇒ circle of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | ||
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| + | == 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. | ||
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<br clear="all"><br> | <br clear="all"><br> | ||
{{Trishapes}} | {{Trishapes}} | ||
{{Rotope Nav|11|12|13|(II)I<br>Cylinder|(II)'<br>Cone|((II)I)<br>Torus|hedra}} | {{Rotope Nav|11|12|13|(II)I<br>Cylinder|(II)'<br>Cone|((II)I)<br>Torus|hedra}} | ||
Revision as of 14:03, 3 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 |
