Sphenocorona (EntityTopic, 14)
From Hi.gher. Space
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 |