Cone (EntityTopic, 11)
From Hi.gher. Space
(Difference between revisions)
(→Equations) |
m |
||
| Line 44: | Line 44: | ||
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. | 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. | ||
| - | + | {{Clear}} | |
{{Trishapes}} | {{Trishapes}} | ||
{{Tapertope Nav|7|8|9|111<br>Cube|2<sup>1</sup><br>Cone|[11]<sup>1</sup><br>Square pyramid|hedra}} | {{Tapertope Nav|7|8|9|111<br>Cube|2<sup>1</sup><br>Cone|[11]<sup>1</sup><br>Square pyramid|hedra}} | ||
Revision as of 20:45, 22 November 2011
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 ⇒ perpendicular 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 = πr(r + √(r2 + h2))
volume = π∕3 · r2h
- The planar cross-sections (n) of a cone are:
[!x,!y] ⇒ isosceles triangle of base length 2r and perpendicular height h
[!z] ⇒ circle of radius (r − nr∕h)
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 Square pyramid |
| List of tapertopes | ||
