In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an bipyramid (by inserting an prism between its congruent halves).
There are three elongated bipyramids that are Johnson solids: Elongated triangular bipyramid (), Elongated square bipyramid (), and Elongated pentagonal bipyramid (). Higher forms can be constructed with isosceles triangles.
Forms Name elongated triangular bipyramid elongated square bipyramidelongated pentagonal bipyramidelongatedhexagonalbipyramidTypeEquilateralIrregularImage Faces 6 triangles,3 squares 8 triangles,4 squares 10 triangles,5 squares 12 triangles,6 squaresDualtriangular bifrustumsquare bifrustumpentagonal bifrustumhexagonal bifrustum
Applications Elongated bipyramids are sometimes used as dice, especially to make dice with atypical side count, such as 5 or 7. Such a die has numbers written on the square faces, which are usually heightened into rectangles for convenience in rolling. Whichever number comes face-up when the die is rolled is the side that is to be read.
See also Gyroelongated bipyramid Gyroelongated pyramid Elongated pyramid Diminished trapezohedron
References Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others. The first proof that there are only 92 Johnson solids.