pentagonal orthocupolarotunda

{{Short description|32nd Johnson solid; pentagonal cupola and rotunda joined base-to-base}}

{{Infobox polyhedron

|image=pentagonal_orthocupolarotunda.png

|type=Johnson
{{math|pentagonal gyrobicupola – J{{sub|32}} – pentagonal gyrocupolarotunda}}

|faces=3×5 triangles
5 squares
2+5 pentagons

|edges=50

|vertices=25

|symmetry={{math|C{{sub|5v}}}}

|vertex_config={{math|10(3.4.3.5)
5(3.4.5.4)
2.5(3.5.3.5)}}

|dual=-

|properties=convex

|net=Johnson solid 32 net.png

}}

In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids ({{math|J{{sub|32}}}}). As the name suggests, it can be constructed by joining a pentagonal cupola ({{math|J{{sub|5}}}}) and a pentagonal rotunda ({{math|J{{sub|6}}}}) along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda ({{math|J{{sub|33}}}}).

{{Johnson solid}}