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Orthobifastigium | |
---|---|
Type | orthobicupola |
Faces | 4 triangles 4 trapezoids |
Edges | 14 |
Vertices | 8 |
Symmetry group | D2h |
Dual polyhedron | self-dual |
Properties | convex |
In geometry, the orthobifastigium (digonal orthobicupola), is formed by gluing together two triangular prisms on their square faces, but without twisting. With regular faces, it has coplanar faces, so it is a limiting case of a Johnson solid. More generally the square can be isosceles trapezoids.
It is topologically a self-dual polyhedron and can also be called an elongated octahedron and self-dual octahedron. [1]
These polyhedra resemble the dual gyrobifastigium in that both shapes have eight vertices and eight faces, with the faces forming a belt of four quadrilaterals separating two pairs of triangles from each other. However, in the dual gyrobifastigium the two pairs of triangles are twisted with respect to each other while in the orthobifastigium they are not.
It can be made with regular faces, squares and triangles, but the triangles will be coplanar.
Regular-faced | Gyrobifastigium |
In geometry, an Archimedean solid is one of 13 convex polyhedra whose faces are regular polygons and whose vertices are all symmetric to each other. They were first enumerated by Archimedes. They belong to the class of convex uniform polyhedra, the convex polyhedra with regular faces and symmetric vertices, which is divided into the Archimedean solids, the five Platonic solids, and the two infinite families of prisms and antiprisms. The pseudorhombicuboctahedron is an extra polyhedron with regular faces and congruent vertices, but it is not generally counted as an Archimedean solid because it is not vertex-transitive. An even larger class than the convex uniform polyhedra is the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices.
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