# Cone (EntityTopic, 11)

(Redirected from Rotope 12)

A cone is a special case of a pyramid where the base is a circle. It is bounded by its circular base and a curved surface

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
total edge length = 2πr
surface area = πr(r + √(r2 + h2))
volume = π3 · r2h
[!x,!y] ⇒ isosceles triangle of base length 2r and perpendicular height h
[!z] ⇒ circle of radius (rnrh)

## 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. 111Cube 8. 21Cone 9. [11]1Square pyramid List of tapertopes