Cone (EntityTopic, 11)
From Higher Dimensions Database
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:
x^{2} + y^{2} = r^{2}
z = 0
- The hypervolumes of a cone are given by:
total edge length = 2πr
surface area = πr(r + √(r^{2} + h^{2}))
volume = ^{π}∕_{3} · r^{2}h
- 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. 2^{1} Cone | 9. [11]^{1} Square pyramid |
List of tapertopes |