Cone (EntityTopic, 11)

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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
total edge length = 2πr
surface area = πr2 + πrsqrt(h2 + r2)
volume = πr2h3-1
[!x,!y] ⇒ Unknown
[!z] ⇒ circle of radius (r-rnh-1)




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

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