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 triangular bifrustum is the second in an infinite series of

bifrustum An ''n''-agonal bifrustum is a polyhedron composed of three parallel planes of ''n''-agons, with the middle plane largest and usually the top and bottom congruent. It can be constructed as two congruent frusta combined across a plane of symmetry ...

polyhedra. It has 6

trapezoid A quadrilateral with at least one pair of parallel sides is called a trapezoid () in American and Canadian English. In British and other forms of English, it is called a trapezium (). A trapezoid is necessarily a convex quadrilateral in Eucli ...

and 2

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colli ...

faces. It may also be called the truncated triangular bipyramid; however, that term is ambiguous, as it may also refer to polyhedra formed by truncating all five vertices of a

triangular bipyramid In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids. It is the dual of the triangular prism with 6 isosceles triangle faces. As the name suggests, i ...

. This polyhedron can be constructed by taking a

and truncating the polar axis vertices, making it into two end-to-end

frustum In geometry, a (from the Latin for "morsel"; plural: ''frusta'' or ''frustums'') is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid. In the case of a pyramid, the base faces are ...

s. It appears as the form of certain

nanocrystal A ''nanocrystal'' is a material particle having at least one dimension smaller than 100 nanometres, based on quantum dots (a nanoparticle) and composed of atoms in either a single- or poly-crystalline arrangement. The size of nanocrystals disti ...

s.. A truncated triangular bipyramid can be constructed by connecting two stacked regular

octahedra In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ...

with 3 pairs of

tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...

around the sides. This represents a portion of the gyrated alternated cubic honeycomb. : Triangulated truncated triangular bipyramid

References

External links

Conway Notation for Polyhedra
Try: t3dP3 Polyhedra {{Polyhedron-stub