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:
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: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind


7. 111
Cube
8. 21
Cone
9. [11]1
Square pyramid
List of tapertopes