A gyroelongated pentagonal birotunda is formed by attaching two pentagonal rotundas to the two decagonal bases of a decagonal antiprism.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 40 polyhedron vertices, 90 polyhedron edges, and 52 faces. The faces
consist of 40 equilateral triangles and 12
regular pentagons (McCooey).
See also
Antiprism,
Birotunda,
Pentagonal Rotunda
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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 Pentagonal Birotunda." https://dmccooey.com/polyhedra/GyroelongatedPentagonalBirotunda.html.Referenced
on Wolfram|Alpha
Gyroelongated Pentagonal
Birotunda
Cite this as:
Weisstein, Eric W. "Gyroelongated Pentagonal
Birotunda." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GyroelongatedPentagonalBirotunda.html
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