Hexagonal bifrustum
Encyclopedia
Hexagonal Bifrustum
Type Bifrustum
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....

Faces 12 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, 2 hexagons
Edges 24
Vertices 18
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...

D6h
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 hexagonal dipyramid
Elongated hexagonal dipyramid
In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid .- Related polyhedra:...

Properties convex


The hexagonal bifrustum or truncated 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...

is the fourth in an infinite series of bifrustum
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....

 polyhedra. It has 12 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...

 and 2 hexagonal faces.

This polyhedron can be constructed by taking a hexagonal dipyramid and truncating the polar axis vertices, making it into two end-to-end frustum
Frustum
In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....

s.

A sapphire
Sapphire
Sapphire is a gemstone variety of the mineral corundum, an aluminium oxide , when it is a color other than red or dark pink; in which case the gem would instead be called a ruby, considered to be a different gemstone. Trace amounts of other elements such as iron, titanium, or chromium can give...

 or ruby
Ruby
A ruby is a pink to blood-red colored gemstone, a variety of the mineral corundum . The red color is caused mainly by the presence of the element chromium. Its name comes from ruber, Latin for red. Other varieties of gem-quality corundum are called sapphires...

 crystal is an example of a hexagonal bifrustum.

It has been used for a decorative polyhedral monthly calendar
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...

, with one month on each trapezoid face. (regular and rhombic
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. Its dual is the cuboctahedron.-Properties:...

dodecahedra have also been used for calendar months.)
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