The Sphenocorona

The sphenocorona is the 86th Johnson solid (J86). Its surface consists of 12 equilateral triangles and 2 squares.

The sphenocorona

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:

Projection Envelope Description

Top view.


Side view.


Front view.

Square faces project to bottom two edges.


The Cartesian coordinates of the sphenocorona with edge length 2 are:

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:

Last updated 26 May 2018.

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