A gyroelongated square cupola is formed by adjoining a square cupola and an octagonal antiprism
along their matching octagonal bases.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 20 polyhedron vertices, 44 polyhedron edges, and 26 faces. The faces
consist of 20 equilateral triangles, 5 squares, and one regular octagon
(McCooey).
It is implemented in the Wolfram Language
as PolyhedronData["GyroelongatedSquareCupola"].
See also
Antiprism,
Cupola,
Gyroelongated Cupola,
Johnson
Solid,
Square Cupola
Explore with Wolfram|Alpha
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. "Gyroelongated Square Cupola." https://dmccooey.com/polyhedra/GyroelongatedSquareCupola.html.Referenced
on Wolfram|Alpha
Gyroelongated Square Cupola
Cite this as:
Weisstein, Eric W. "Gyroelongated Square Cupola."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GyroelongatedSquareCupola.html
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