# Category: Prismatoid polyhedra

Pentagrammic antiprism
In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams. It has 12 faces, 20 e
Hendecagonal prism
In geometry, the hendecagonal prism is one in an infinite set of convex prisms formed by square sides and two regular polygon caps, in this case two hendecagons.So, it has 2 hendecagons and 11 squares
Octagrammic antiprism
In geometry, the octagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two octagrams.
Square cupola
In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids (J4). It can be obtained as a slice of the rhombicuboctahedron. As in all cupolae, the base polygon has twice
Crossed pentagonal cuploid
In geometry, the crossed pentagonal cupoloid or crossed pentagonal semicupola is one member of the infinite family of cuploids. It can be obtained as a slice of the great complex rhombicosidodecahedro
Decagrammic antiprism
In geometry, the decagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two decagrams.
Decagrammic prism
In geometry, the decagrammic prism is one of an infinite set of nonconvex prisms formed by squares sides and two regular star polygon caps, in this case two decagrams. It has 12 faces (10 squares and
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges a
Square antiprism
In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube. I
Pentagonal prism
In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices.
Octagonal prism
In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps. If faces are all regular, it is a semiregular polyhedron.
Heptagonal prism
In geometry, the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces, 21 edges, and 14 vertices.
Pentagonal antiprism
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of two pentagons joine
Prismatoid
In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both planes have the same number of vertices, and the late
Hexagonal antiprism
In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms exce
Triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangul
Cupola (geometry)
In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles ar
Heptagrammic cupola
In geometry, the heptagrammic cupola is a star-cupola made from a heptagram, {7/3} and parallel tetradecagram, {14/3}, connected by 7 mutually intersecting equilateral triangles and squares.
Octagrammic cupola
In geometry, the octagrammic cupola is a star-cupola made from an octagram, {8/3} and parallel hexadecagram, {16/3}, connected by 8 equilateral triangles and squares.
Triangular cupola
In geometry, the triangular cupola is one of the Johnson solids (J3). It can be seen as half a cuboctahedron. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon
Pentagrammic prism
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams. It is a special case of a right
Decagonal antiprism
In geometry, the decagonal antiprism is the eighth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms e
Pentagrammic crossed-antiprism
In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams. It differs fr
Octagrammic prism
In geometry, the octagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two octagrams. * v * t * e
Wedge (geometry)
In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices. A wedge is a subclass of the prismatoids with the b
Pyramid (geometry)
In geometry, a pyramid (from Greek πυραμίς (pyramís)) is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The
Pentagrammic cuploid
In geometry, the pentagrammic cuploid or pentagrammmic semicupola is the simplest of the infinite family of cuploids. It can be obtained as a slice of the small complex rhombicosidodecahedron. As in a
Square pyramid
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C4v symmetry. If all edge lengths
Apeirogonal prism
In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane. Thorold Gosset called it a 2-
Heptagonal antiprism
In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms e
Crossed pentagrammic cupola
In geometry, the crossed pentagrammic cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex pentagonal cupola. It can be obtained as a slice of the great
Prism (geometry)
In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all para
Octagrammic crossed-antiprism
In geometry, the octagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two octagrams.
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five
Rhombohedron
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped wher
Apeirogonal antiprism
In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane. If the sides are
Parallelepiped
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as
Hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the
Hexagonal pyramid
In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual. A right he
Enneagonal antiprism
In geometry, the enneagonal antiprism (or nonagonal antiprism) is one in an infinite set of convex antiprisms formed by triangle sides and two regular polygon caps, in this case two enneagons. Antipri
Decagonal prism
In geometry, the decagonal prism is the eighth in the infinite set of prisms, formed by ten square side faces and two regular decagon caps. With twelve faces, it is one of many nonregular dodecahedra.
Enneagonal prism
In geometry, the enneagonal prism (or nonagonal prism) is the seventh in an infinite set of prisms, formed by square sides and two regular enneagon caps. If faces are all regular, it is a semiregular
Octagonal antiprism
In geometry, the octagonal antiprism is the 6th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms exce
Pentagonal cupola
In geometry, the pentagonal cupola is one of the Johnson solids (J5). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares,
Pentagonal pyramid
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual. The regular penta
Crossed square cupola
In geometry, the crossed square cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex square cupola. It can be obtained as a slice of the nonconvex great
Prismatic uniform polyhedron
In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms. All have their vertices
Dodecagonal prism
In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps. If faces are all regular, it is a uniform polyhedron.
Hyperrectangle
In geometry, an orthotope (also called a hyperrectangle or a box) is the generalization of a rectangle to higher dimensions.A necessary and sufficient condition is that it is congruent to the Cartesia
Octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equi
Pentaprism
A pentaprism is a five-sided reflecting prism used to deviate a beam of light by a constant 90°, even if the entry beam is not at 90° to the prism.The beam reflects inside the prism twice, allowing th
Antiprism
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. The
Frustum
In geometry, a frustum (from the Latin for "morsel"; plural: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid. In t