Bifrustum
Encyclopedia
Set of bifrustums or Truncated bipyramids |
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Faces | 2 n-gon Polygon In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments... s, 2n trapezoid Trapezoid In Euclidean geometry, a convex quadrilateral with one pair of parallel sides is referred to as a trapezoid in American English and as a trapezium in English outside North America. A trapezoid with vertices ABCD is denoted... s |
Edges | 5n |
Vertices | 3n |
Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation... |
Dnh |
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... |
Elongated bipyramids |
Properties | convex |
An n-agonal bifrustum (or truncated bipyramid) is a polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
composed of three parallel planes of n-agons
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
, with the middle plane largest and usually the top and bottom congruent.
It can be constructed as two congruent frusta
Frustum
In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....
combined across a plane of symmetry, and also as a bipyramid
Bipyramid
An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.The referenced n-gon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves.The...
with the two polar vertices truncated.
They are duals
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 family of elongated bipyramids.
Forms
Triangular bifrustum Triangular bifrustum The triangular bifrustum or triangular truncated bipyramid is the second in an infinite series of bifrustum polyhedra. It has 6 trapezoid and 2 triangle faces.... - 6 trapezoids, 2 triangles, dual elongated triangular dipyramid Elongated triangular dipyramid In geometry, the elongated triangular bipyramid is one of the Johnson solids , convex polyhedra whose faces are regular polygons... |
Square bifrustum Square bifrustum The square bifrustum or square truncated bipyramid is the second in an infinite series of bifrustum polyhedra. It has 4 trapezoid and 2 square faces.... - 8 trapezoids, 2 squares, dual elongated square dipyramid Elongated square dipyramid In geometry, the elongated square bipyramid is one of the Johnson solids . As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves.... |
Pentagonal bifrustum Pentagonal bifrustum The pentagonal bifrustum or pentagonal truncated bipyramid is the third in an infinite series of bifrustum polyhedra. It has 10 trapezoid and 2 pentagonal faces. It is the dual of the Johnson solid, elongated pentagonal dipyramid.... - 10 trapezoids, 2 pentagons, dual elongated pentagonal dipyramid Elongated pentagonal dipyramid In geometry, the elongated pentagonal bipyramid is one of the Johnson solids . As the name suggests, it can be constructed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its congruent halves.... |
Hexagonal bifrustum Hexagonal bifrustum The hexagonal bifrustum or truncated bipyramid is the fourth in an infinite series of bifrustum polyhedra. It has 12 trapezoid and 2 hexagonal faces.... - 12 trapezoids, 2 hexagons, dual elongated hexagonal dipyramid Elongated hexagonal dipyramid In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid .- Related polyhedra:... |
In general, a n-agonal bifrustum has 2n trapezoids, 2 n-agons, and is dual to the elongated dipyramid
Elongated dipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid ....
s.