In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by joining a pentagonal cupola () and a pentagonal rotunda () along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda (). Formulae The following formulae for volume and surface area can be used if all faces are regular, with edge length a: References External links Johnson solids