The Augmented Sphenocorona
The augmented sphenocorona is the 87th Johnson solid (J87). Its surface consists of 16 equilateral triangles and 1 square, for a total of 17 faces, 26 edges, and 11 vertices.
It is constructed by augmenting one of the square faces of the sphenocorona (J86) with a square pyramid. The triangular face of the augment that touches the remaining square face is very nearly coplanar: their dihedral angle is approximately 171.8°.
Projections
Here are some views of the augmented sphenocorona from various angles:
Projection  Description 

Top view. 

Side view. 

Front view. 

45° side view. 

Parallel to line from augment apex to upper left vertex. 
Coordinates
The Cartesian coordinates of the augmented sphenocorona with edge length 2 are:
 (0, 0, ±1)
 (±A, √B, ±1)
 (0, √C, ±D)
 (±1, √E, 0)
 ((A+B√2)/2, (B−A√2)/2, 0)
where A, B, C, D, and E are roots of the following polynomials within the given ranges:
15A^{4} − 24A^{3} − 100A^{2} + 112A + 92 = 0,  1≤A≤2 
225B^{4} − 24B^{3} − 3176B^{2} − 96B + 3600 = 0,  1≤B≤2 
225C^{4} − 24C^{3} − 3176C^{2} − 96C + 3600 = 0,  3≤C≤4 
15D^{4} − 36D^{3} − 82D^{2} + 100D + 95 = 0,  1≤D≤2 
E^{2} − 4E − 20 = 0  6≤E≤7 
Note that B and C are different roots of the same polynomial. E has the closedform expression 2+2√6.
The approximate numerical values are:
 A = 1.705453885692834
 √B = 1.044713857367277
 √C = 1.914399800381786
 D = 1.578855253321743
 √E = 2.626590848527109