Concept
Elongated pyramid
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual. There are three elongated pyramids that are Johnson solids: Elongated triangular pyramid (J_7), Elongated square pyramid (J_8), and Elongated pentagonal pyramid (J_9). Higher forms can be constructed with isosceles triangles.
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Related concepts (5)
Elongated bipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid (by inserting an n-gonal prism between its congruent halves). There are three elongated bipyramids that are Johnson solids: Elongated triangular bipyramid (J_14), Elongated square bipyramid (J_15), and Elongated pentagonal bipyramid (J_16). Higher forms can be constructed with isosceles triangles.
Diminished trapezohedron
In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the polar vertices of a trapezohedron and replacing it by a new face (diminishment). It has one regular n-gonal base face, n triangle faces around the base, and n kites meeting on top. The kites can also be replaced by rhombi with specific proportions. Along with the set of pyramids and elongated pyramids, these figures are topologically self-dual.
Gyroelongated bipyramid
In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid by inserting an n-gonal antiprism between its congruent halves. Two members of the set can be deltahedra, that is, constructed entirely of equilateral triangles: the gyroelongated square bipyramid, a Johnson solid, and the icosahedron, a Platonic solid. The gyroelongated triangular bipyramid can be made with equilateral triangles, but is not a deltahedron because it has coplanar faces, i.
