In
geometry, the gyroelongated pyramids (also called ''augmented
antiprisms'') are an infinite set of
polyhedra, constructed by adjoining an
pyramid to an
antiprism.
There are two ''gyroelongated pyramids'' that are
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
s made from regular triangles and square, and pentagons. A triangular and hexagonal form can be constructed with
coplanar faces. Others can be constructed allowing for
isosceles triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...
s.
Forms
See also
*
Gyroelongated bipyramid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson ...
*
Elongated bipyramid
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:
* Elongat ...
*
Elongated pyramid
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an pyramid to an prism. Along with the set of pyramids, these figures are topologically self-dual.
There are three ''elongated pyramids'' that are ...
*
Diminished trapezohedron
References
*
Norman W. Johnson
Norman Woodason Johnson () was a mathematician at Wheaton College, Norton, Massachusetts.
Early life and education
Norman Johnson was born on in Chicago. His father had a bookstore and published a local newspaper.
Johnson earned his unde ...
, "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.
Pyramids and bipyramids
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