| 5-sided trapezohedron |
Click on picture for large version. | | Type | Trapezohedron | | Faces | 2n kites | | Edges | 4n | | Vertices | 2n+2 | | Face configuration | n,3,3,3 | | Symmetry group | Dnd | | Dual polyhedron | antiprism | | Properties | convex, semi-regular (face-uniform) | The n-sided trapezohedron or deltohedron is the dual polyhedron of a regular n-sided antiprism. Its 2n faces are congruent kites, also called deltoids (not trapezoids, so the name trapezohedron is misleading). Download high resolution version (452x773, 37 KB)Pentagonal antiprism, made by me using POV-Ray, see image:poly. ...
A separate article is about kite flying. ...
The symmetry group of an object (e. ...
The symmetry group of an object (e. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles. ...
See also: congruence relation In geometry, two shapes are called congruent if one can be transformed into the other by a series of translations, rotations and reflections. ...
A separate article is about kite flying. ...
A trapezoid (American English) or trapezium (British English) is a quadrilateral two of whose sides are parallel to each other. ...
The name deltohedron should not be confused with deltahedron. The triaugmented triangular prism, a convex deltahedron A deltahedron is a polyhedron where all the faces are equilateral triangles The name arises from the fact that an equilateral triangle is the shape of the Greek majuscule delta (Δ). ...
An n-sided trapezohedron can be decomposed into two equal n-sided pyramids and an n-sided antiprism. An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles. ...
This is also the shape of 10 sided dice commonly used in the dungeons and dragons roleplaying game. Rolling dice A die (Old French de, from Latin datum something given or played [1]) is a small polyhedral object (usually a cube) suitable as a gambling device (especially for craps or sic bo). ...
The original Dungeons & Dragons set Dungeons & Dragons (abbreviated as D&D or DnD) is a fantasy role-playing game (RPG) published by Gary Gygax and David Arneson in January 1974. ...
This article is about traditional role-playing games. ...
In the case of the dual of a regular triangular antiprism the kites are rhombi, hence these trapezohedra are also zonohedra. They are called rhombohedron. They are cubes scaled in the direction of a body diagonal. Also they are the parallelepipeds with congruent rhombic faces. A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
Cube may denote one of the following. ...
In geometry, a parallelepiped or parallelopipedon is a 3-dimensional figure that can be thought of as an (impractical) box that, while not necessarily having right angles, still has its upper surface level whenever it rests its lower surface on something level. ...
A special case of a rhombohedron is one of the which the rhombi which form the faces have angles of 60° and 120°. It can be decomposed into two equal regular tetrahedra and a regular octahedron. Since parallelepipeds can fill space, so can a combination of regular tetrahedra and regular octahedra. An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
A tessellated plane A tessellation of the plane is a collection of plane figures that fill the plane with no overlaps and no gaps. ...
The symmetry group of an n-sided trapezohedron is Dnd of order 4n, except in the case of a cube, which has the larger symmetry group Od of order 48, which has four versions of D3d as subgroups. The symmetry group of an object (e. ...
The rotation group is Dn of order 2n, except in the case of a cube, which has the larger rotation group O of order 24, which has four versions of D3 as subgroups. In mechanics and geometry, the rotation group is the set of all rotations of 3-dimensional Euclidean space, R3. ...
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