In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the orthobifastigium (
digon
In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visua ...
al ortho
bicupola), is formed by gluing together two
triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is ''oblique''. A unif ...
s on their square faces, but without twisting. With regular faces, it has coplanar faces, so it is a limiting case of a
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
. More generally the square can be
isosceles trapezoid
In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined ...
s.
It is topologically a
self-dual polyhedron
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. ...
and can also be called an
elongated octahedron
In geometry, an elongated octahedron is a polyhedron with 8 faces (4 triangle, triangular, 4 isosceles trapezoidal), 14 edges, and 8 vertices.
As a deltahedral hexadecahedron
A related construction is a hexadecahedron, 16 triangular face (ge ...
and ''self-dual octahedron''.
These polyhedra resemble the dual
gyrobifastigium
In geometry, the gyrobifastigium is the 26th Johnson solid (). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is the only Johnson solid that can tile ...
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.
Regular-faced
It can be made with regular faces, squares and triangles, but the triangles will be coplanar.
See also
*
Elongated octahedron
In geometry, an elongated octahedron is a polyhedron with 8 faces (4 triangle, triangular, 4 isosceles trapezoidal), 14 edges, and 8 vertices.
As a deltahedral hexadecahedron
A related construction is a hexadecahedron, 16 triangular face (ge ...
References
External links
{{Johnson solids navigator
Space-filling polyhedra