# Bicone (EntityTopic, 10)

### From Hi.gher. Space

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| image=<[#embed [hash RQBYTBGJKTVCMV1MDFX1TTA2C5] [width 180]]> | | image=<[#embed [hash RQBYTBGJKTVCMV1MDFX1TTA2C5] [width 180]]> | ||

| dim=3 | | dim=3 | ||

- | | elements=2, 1, 2 | + | | elements=2 conic naps, 1 circular edge, 2 [[point]]s |

| genus=0 | | genus=0 | ||

| ssc=<(xy)z> | | ssc=<(xy)z> | ||

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| extra={{STS Bracketope | | extra={{STS Bracketope | ||

| index=8 | | index=8 | ||

+ | | notation=<(II)I> | ||

}}}} | }}}} | ||

- | A '''bicone''' is the [[tegum product]] of a [[circle]] and a [[digon]]. | + | A '''bicone''' is the [[tegum product]] of a [[circle]] and a [[digon]]. It is also the result of attaching two [[cone]]s at their bases. |

+ | == Equations == | ||

+ | *Variables: | ||

+ | <blockquote>''r'' ⇒ radius of base of bicone<br> | ||

+ | ''h'' ⇒ perpendicular height of bicone from the circle to one of the vertices</blockquote> | ||

+ | |||

+ | *The [[hypervolume]]s of a cone are given by: | ||

+ | <blockquote>total edge length = 2π''r''<br> | ||

+ | surface area = 2π''r''√(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br> | ||

+ | volume = {{Over|2π|3}} · ''r''<sup>2</sup>''h''</blockquote> | ||

+ | |||

+ | *The [[planar]] [[cross-section]]s (''n'') of a cone are: | ||

+ | <blockquote>[!x,!y] ⇒ rhombus <br> | ||

+ | [!z] ⇒ circle | ||

+ | </blockquote> | ||

{{Trishapes}} | {{Trishapes}} | ||

{{Bracketope Nav|7|8|9|[(II)I]<br>Cylinder|<(II)I><br>Bicone|([II]I)<br>Crind|hedra}} | {{Bracketope Nav|7|8|9|[(II)I]<br>Cylinder|<(II)I><br>Bicone|([II]I)<br>Crind|hedra}} |

## Revision as of 02:32, 26 March 2017

A **bicone** is the tegum product of a circle and a digon. It is also the result of attaching two cones at their bases.

## Equations

- Variables:

r⇒ radius of base of bicone

h⇒ perpendicular height of bicone from the circle to one of the vertices

- The hypervolumes of a cone are given by:

total edge length = 2πr

surface area = 2πr√(r^{2}+h^{2}))

volume =^{2π}∕_{3}·r^{2}h

- The planar cross-sections (
*n*) of a cone are:

[!x,!y] ⇒ rhombus

[!z] ⇒ circle

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. [(II)I] Cylinder | 8. <(II)I>
Bicone | 9. ([II]I) Crind |

List of bracketopes |