Tetragonal trapezohedron
Encyclopedia
| Tetragonal trapezohedron | |
|---|---|
 Click on picture for large version. |
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| Type | trapezohedra |
| Faces | 8 kites Kite (geometry) In Euclidean geometry a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are next to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite each other rather than next to each other... |
| Edges | 16 |
| Vertices | 10 |
| 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.... |
4,3,3,3 |
| Symmetry group | D4d, [2+,8], (2*4) |
| 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... |
Square antiprism Square antiprism In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps... |
| Properties | convex, face-transitive |
The tetragonal 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 second 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 eight 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...
kites
Kite (geometry)
In Euclidean geometry a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are next to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite each other rather than next to each other...
.