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The pentagonal cupola is Johnson solid 
. Its faces consist of 5 equilateral triangles, 5 squares,
one pentagon, and one decagon.
It is therefore a (non-regular) dodecahedron.
The surface area and volume of the triangular cupola with unit edge lengths are
 |  | ![1/4[20+sqrt(10(80+31sqrt(5)+sqrt(2175+950sqrt(5))))]](/images/equations/PentagonalCupola/Inline4.svg) |
(1)
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(2)
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