In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
In geometry, the triangular cupola is one of the Johnson solids. It can be seen as half a cuboctahedron.
In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids. It can be obtained as a slice of the rhombicuboctahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; in this case the base polygon is an octagon.
In geometry, the pentagonal rotunda is one of the Johnson solids. It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces.
In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J42) with one pentagonal rotunda removed.
In geometry, the square gyrobicupola is one of the Johnson solids. Like the square orthobicupola, it can be obtained by joining two square cupolae along their bases. The difference is that in this solid, the two halves are rotated 45 degrees with respect to one another.
In geometry, the elongated pentagonal gyrobirotunda is one of the Johnson solids. As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron, by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda.
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.
In geometry, the triangular hebesphenorotunda is one of the Johnson solids.
In geometry, the elongated pentagonal cupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal cupola by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola with its "lid" removed.
In geometry, the gyrobifastigium is the 26th Johnson solid. It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is the only Johnson solid that can tile three-dimensional space.
In geometry, the pentagonal orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by joining two pentagonal cupolae along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola.
In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal orthobicupola by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola.
In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola.
In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.
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.
In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids. Like the pentagonal orthocupolarotunda, it can be constructed by joining a pentagonal cupola and a pentagonal rotunda along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
In geometry, the elongated triangular gyrobicupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a "triangular gyrobicupola," or cuboctahedron, by inserting a hexagonal prism between its two halves, which are congruent triangular cupolae. Rotating one of the cupolae through 60 degrees before the elongation yields the triangular orthobicupola.
In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola or the pentagonal rotunda through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda.
In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda by inserting a decagonal prism between its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the prism yields an elongated pentagonal gyrocupolarotunda.
