The sphenocorona is the 86th Johnson solid (J86). Its surface consists of 12 equilateral triangles and 2 squares.
The sphenocorona is one of the special Johnson solids at the end of Norman Johnson's list that are not directly derived from the uniform polyhedra by cut-and-paste operations.
Here are some views of the sphenocorona from various angles:
Square faces project to bottom two edges.
The Cartesian coordinates of the sphenocorona with edge length 2 are:
- (0, 0, ±1)
- (±A, √B, ±1)
- (0, √C, ±D)
- (±1, √E, 0)
where A, B, C, D, and E are roots of the following polynomials within the given ranges:
|15A4 - 24A3 - 100A2 + 112A + 92 = 0,||1≤A≤2|
|225B4 - 24B3 - 3176B2 - 96B + 3600 = 0,||1≤B≤2|
|225C4 - 24C3 - 3176C2 - 96C + 3600 = 0,||3≤C≤4|
|15D4 - 36D3 - 82D2 + 100D + 95 = 0,||1≤D≤2,|
|E2 - 4E - 20 = 0||6≤E≤7|
Note that B and C are different roots of the same polynomial. E has the closed-form expression 2+2√6.
The approximate numerical values are:
- A = 1.705453885692834
- √B = 1.044713857367277
- √C = 1.914399800381786
- D = 1.578855253321743
- √E = 2.626590848527109