Trigonal trapezohedron
Encyclopedia
| Trigonal trapezohedron | |
|---|---|
 Click on picture for large version. |
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| Type | trapezohedra |
| Faces | 6 rhombi Rhombus In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every... |
| Edges | 12 |
| Vertices | 8 |
| Face configuration Face configuration In geometry, a face configuration is notational description of a face-transitive polyhedron. It represents a sequential count of the number of faces that exist at each vertex around a face.... |
3,3,3,3 |
| Symmetry group | D3d, [2+,6], (2*3) |
| Dual polyhedron Dual polyhedron In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another... |
trigonal antiprism Antiprism In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles... |
| Properties | convex, face-transitive |
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the trigonal trapezohedron
Trapezohedron
The n-gonal trapezohedron, antidipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. Its 2n faces are congruent kites . The faces are symmetrically staggered.The n-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry...
or deltohedron is the first in an infinite series of face-uniform polyhedra which are dual
Dual polyhedron
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...
to the antiprism
Antiprism
In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles...
s. It has six faces which are congruent
Congruence (geometry)
In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...
rhombi
Rhombus
In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every...
.
Trigonal trapezohedrons are a subset of the rhombohedron
Rhombohedron
In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi. It is a special case of a parallelepiped where all edges are the same length....
s. The cube
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 can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
is a special case with square faces.