Cone (EntityTopic, 11)
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| - | <[#ontology [kind topic] [cats 3D Curved Tapertope]]> | + | <[#ontology [kind topic] [cats 3D Curved Tapertope] [alt [[freebase:03bzp0]] [[wikipedia:Cone_(geometry)]]]]> |
{{STS Shape | {{STS Shape | ||
| - | | image=<[# | + | | image=<[#embed [hash 5YKZM3N2DR4ZGBBREJKXT1AV1Q] [width 180]]> |
| dim=3 | | dim=3 | ||
| - | | elements= | + | | elements=1 [[circle]], 1 conical nap, 1 circular edge, 1 [[point]] |
| genus=0 | | genus=0 | ||
| ssc=(xy)P | | ssc=(xy)P | ||
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}}}} | }}}} | ||
| - | A '''cone''' is a special case of a [[pyramid]] where the base is a [[circle]]. | + | 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]] [[polyhedron|polyhedra]] that satisfy [[Euler's formula|Euler's F + V = E + 2]]. | The cone is one of the few [[curved]] [[polyhedron|polyhedra]] that satisfy [[Euler's formula|Euler's F + V = E + 2]]. | ||
Latest revision as of 14:29, 26 March 2017
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
- 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 | ||
