# Sphenocorona (EntityTopic, 14)

### From Hi.gher. Space

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:C = 1.914399800381786 | :C = 1.914399800381786 | ||

:D = 1.578855253321743 | :D = 1.578855253321743 | ||

- | :E =2.626590848527109 | + | :E = 2.626590848527109 |

== Images == | == Images == |

## Latest revision as of 01:20, 10 February 2018

The **sphenocorona** is the 86th Johnson solid, J86.

## Cartesian coordinates

The Cartesian coordinates of the sphenocorona, resting on the origin and with edge length 2, are:

- (0, 0, ±1)
- (±A, B, ±1)
- (0, C, ±D)
- (±1, E, 0)

where A, B, C, D, E are roots of the following polynomials:

92 + 112A - 100A² - 24A³ + 15A⁴ 1 < A < 2 3600 - 96B² - 3176B⁴ - 24B⁶ + 225B⁸ 1 < B < 1.5 3600 - 96C² - 3176C⁴ - 24C⁶ + 225C⁸ 1.5 < C < 2 95 + 100D - 82D² - 36D³ + 15D⁴ 1 < D < 2 -20 - 4E² + E⁴ 1 < E < 2

Or, in closed form:

- A = (1/15)(6 + √6 + 2√(213 - 57√6))
- B = (2/5)√(1/6 + 6√6 - (1/3)√(538 + 18√6))
- C = (2/5)√(1/6 + 6√6 + (1/3)√(538 + 18√6))
- D = (1/15)(9 - √6 + 2√(213 - 57√6))
- E = √(2(1 + √6))

Their numerical values are approximately:

- A = 1.705453885692834
- B = 1.044713857367277
- C = 1.914399800381786
- D = 1.578855253321743
- E = 2.626590848527109

## Images

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 |