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 elongated square cupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a square cupola by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" 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 gyroelongated square bicupola is one of the Johnson solids. As the name suggests, it can be constructed by gyroelongating a square bicupola by inserting an octagonal antiprism between its congruent halves.
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 elongated triangular pyramid is one of the Johnson solids. As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Like any elongated pyramid, the resulting solid is topologically self-dual.
In geometry, the elongated square pyramid is one of the Johnson solids. As the name suggests, it can be constructed by elongating a square pyramid by attaching a cube to its square base. Like any elongated pyramid, it is topologically self-dual.
In geometry, the elongated triangular bipyramid or triakis triangular prism is one of the Johnson solids, convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid by inserting a triangular prism between its congruent halves.
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 triangular cupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a triangular cupola by attaching a hexagonal prism to its base.
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 triangular orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by attaching two triangular cupolas along their bases. It has an equal number of squares and triangles at each vertex; however, it is not vertex-transitive. It is also called an anticuboctahedron, twisted cuboctahedron or disheptahedron. It is also a canonical polyhedron.
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 gyroelongated triangular bicupola is one of the Johnson solids. As the name suggests, it can be constructed by gyroelongating a triangular bicupola by inserting a hexagonal antiprism between its congruent halves.
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.
