Elongated pentagonal cupola

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In geometry, the elongated pentagonal cupola is one of the Johnson solids ( J20 ). As the name suggests, it can be constructed by elongating a pentagonal cupola ( J5 ) by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola ( J38 ) with its "lid" (another pentagonal cupola) removed.

Formulas

The following formulas for the volume and surface area can be used if all faces are regular, with edge length a:

Dual polyhedron

The dual of the elongated pentagonal cupola has 25 faces: 10 isosceles triangles, 5 kites, and 10 quadrilaterals.

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