Edges 60 Vertex configuration 20(3.4)10(3.4.5.4) | Vertices 30 Symmetry group D5d | |
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Type JohnsonJ38 - J39 - J40 Faces 10 triangles2.10 squares2 pentagons | ||
In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids (J39). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola (J31) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae (J5) through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola (J38).
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a: