Elongated pentagonal cupola

In geometry, the elongated pentagonal cupola is one of the Johnson solids (J_20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J_5) by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola (J_38) with its "lid" (another pentagonal cupola) removed. The following formulas for the volume and surface area can be used if all faces are regular, with edge length a: The dual of the elongated pentagonal cupola has 25 faces: 10 isosceles triangles, 5 kites, and 10 quadrilaterals.