An elongated square cupola is formed by adjoining a square cupola and an octagonal prism along their
matching octagonal bases.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 20 polyhedron vertices, 36 polyhedron edges, and 18 faces. The faces
consist of 4 equilateral triangles, 13 squares, and one regular octagon
(McCooey).
See also
Elongated Cupola,
Square
Cupola
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References
Johnson, N. W. "Convex Polyhedra with Regular Faces." Canad. J. Math. 18, 169-200, 1966. https://doi.org/10.4153/CJM-1966-021-8.McCooey,
D. I. "Elongated Square Cupola." https://dmccooey.com/polyhedra/ElongatedSquareCupola.html.Referenced
on Wolfram|Alpha
Elongated Square Cupola
Cite this as:
Weisstein, Eric W. "Elongated Square Cupola."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ElongatedSquareCupola.html
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