Pentagonal cupola explained

Type:	Johnson
Edges:	25
Vertices:	15
Symmetry:	C _{v}
Vertex Config:	10 x ( 3 x 4 x 10 ) 5 x ( 3 x 4 x 5 x 4 )
Net:	Pentagonal Cupola.PNG

In geometry, the pentagonal cupola is one of the Johnson solids . It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.

Properties

The pentagonal cupola's faces are five equilateral triangles, five squares, one regular pentagon, and one regular decagon. It has the property of convexity and regular polygonal faces, from which it is classified as the fifth Johnson solid. This cupola produces two or more regular polyhedrons by slicing it with a plane, an elementary polyhedron's example.

R , and height h , surface area A , and volume V may be applied if all faces are regular with edge length a :C _{5v} of order ten.

Related polyhedron

J _{20} , gyroelongated pentagonal cupola J _{24} , pentagonal orthobicupola J _{30} , pentagonal gyrobicupola J _{31} , pentagonal orthocupolarotunda J _{32} , pentagonal gyrocupolarotunda J _{33} , elongated pentagonal orthobicupola J _{38} , elongated pentagonal gyrobicupola J _{39} , elongated pentagonal orthocupolarotunda J _{40} , gyroelongated pentagonal bicupola J _{46} , gyroelongated pentagonal cupolarotunda J _{47} , augmented truncated dodecahedron J _{68} , parabiaugmented truncated dodecahedron J _{69} , metabiaugmented truncated dodecahedron J _{70} , triaugmented truncated dodecahedron J _{71} , gyrate rhombicosidodecahedron J _{72} , parabigyrate rhombicosidodecahedron J _{73} , metabigyrate rhombicosidodecahedron J _{74} , and trigyrate rhombicosidodecahedron J _{75} . Relatedly, a construction from polyhedra by removing one or more pentagonal cupolas is known as diminishment: diminished rhombicosidodecahedron J _{76} , paragyrate diminished rhombicosidodecahedron J _{77} , metagyrate diminished rhombicosidodecahedron J _{78} , bigyrate diminished rhombicosidodecahedron J _{79} , parabidiminished rhombicosidodecahedron J _{80} , metabidiminished rhombicosidodecahedron J _{81} , gyrate bidiminished rhombicosidodecahedron J _{82} , and tridiminished rhombicosidodecahedron J _{83}