A gyroelongated square pyramid is formed by adjoining a square pyramid and a square antiprism along a common
square base.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 9 polyhedron vertices, 20 polyhedron edges, and 13 faces. The faces
consist of 12 equilateral triangles and one
square (McCooey).
See also
Gyroelongated Pyramid,
Square Antiprism,
Square
Pyramid
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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. "Gyroelongated Square Pyramid." https://dmccooey.com/polyhedra/GyroelongatedSquarePyramid.html.Referenced
on Wolfram|Alpha
Gyroelongated Square Pyramid
Cite this as:
Weisstein, Eric W. "Gyroelongated Square Pyramid."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GyroelongatedSquarePyramid.html
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