Prismatoid polyhedra

A cube is a three-dimensional solid object in geometry. A cube has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron.

geometrical shape

thumb|A tetrahedron.

geometric shape, a polyhedron with an n-sided polygonal base

{| class=wikitable align="right" !bgcolor=#e7dcc3 colspan=2|Parallelepiped |- |align=center colspan=2|240px|Parallelepiped |- |bgcolor=#e7dcc3|Type||PrismPlesiohedron |- |bgcolor=#e7dcc3|Faces||6 parallelograms |- |bgcolor=#e7dcc3|Edges||12 |- |bgcolor=#e7dcc3|Vertices||8 |- |bgcolor=#e7dcc3|Symmetry group||Ci, [2+,2+], (×), order 2 |- |bgcolor=#e7dcc3|Properties||convex, zonohedron |}

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|Rhombohedron |- |align=center colspan=2|240px|Rhombohedron |- |bgcolor=#e7dcc3|Type||prism |- |bgcolor=#e7dcc3|Faces||6 rhombi |- |bgcolor=#e7dcc3|Edges||12 |- |bgcolor=#e7dcc3|Vertices||8 |- |bgcolor=#e7dcc3|Symmetry group||Ci , [2+,2+], (×), order 2 |- |bgcolor=#e7dcc3|Properties||convex, equilateral, zonohedron, parallelohedron |}

thumb|Octagonal antiprism In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .

In geometry, a ; or frustums), often incorrectly spelled as frustrum or frustrums, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an oblique frustum.

pyramid having a square base

right|thumb|240px|Prismatoid with parallel faces and , midway cross-section , and height .

Platonic solid

thumb|right|300px|A pentaprism. right|thumb|300px|A perspective drawing showing a roof pentaprism commonly used in a single lens reflex camera (SLR). The image is flipped laterally by the prism. 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 the transmission of an image through a right angle without inverting it (that is, without changing the image's handedness) as an ordinary right-angle prism or mirror would.

three-sided prism

Johnson solid

pyramid having a pentagonal base

Johnson solid

solid formed by joining two polygons, one with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles

Johnson solid

polyhedron defined by two triangles and three trapezoid faces

prism with a pentagonal base

prism with hexagonal base

solid with 10 faces

antiprism formed by two pentagons joined to each other by a ring of 10 triangles

thumb|Example of a hexahedronIn geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.

thumb|Projections of k-cells onto the plane (from k\in\{1,\dots{},6\}). Only the edges of the higher-dimensional cells are shown. In geometry, a hyperrectangle (also called a box, hyperbox, k-cell or orthotope), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a k-dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k-cell is compact.

antiprism

sixth in an infinite set of prisms, formed by square sides and two regular octagon caps

polyhedron with 7 faces

polyhedron with 9 faces

uniform polyhedron with dihedral symmetry

12-sided box

3d shape

fifth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps

prism with an infinite-sided polygon base