geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, the gyroelongated bipyramids are an infinite set of

polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...

, constructed by elongating an

bipyramid In geometry, a bipyramid, dipyramid, or double pyramid is a polyhedron formed by fusing two Pyramid (geometry), pyramids together base (geometry), base-to-base. The polygonal base of each pyramid must therefore be the same, and unless otherwise ...

by inserting an

antiprism In geometry, an antiprism or is a polyhedron composed of two Parallel (geometry), parallel Euclidean group, direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway po ...

between its congruent halves.

Forms

Three members of the set can be

deltahedra A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter Delta (letter), delta resembling a triangular shape Δ. Deltahedra can be categorized by the prope ...

, that is, constructed entirely of

equilateral triangle An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the ...

s: the

gyroelongated square bipyramid In geometry, the gyroelongated square bipyramid is a polyhedron with 16 triangular faces. it can be constructed from a square antiprism by attaching two equilateral square pyramid, equilateral square pyramids to each of its square faces. The same ...

, a

Johnson solid In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, s ...

; the

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...

, a

Platonic solid In geometry, a Platonic solid is a Convex polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (id ...

; and the '' gyroelongated triangular bipyramid'' if it is made with equilateral triangles, but because it has coplanar faces is not strictly convex. With pairs of triangles merged into rhombi, it can be seen as a

trigonal trapezohedron In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped faces faces is a rhombohedron. An alternative name for the same shape is the ''trig ...

. The other members can be constructed with isosceles triangles.

Use

Pentagonal Gyroelongated Bipyramid * The Pentagonal gyroelongated bipyramid is commonly used in

3D modeling In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based Computer representation of surfaces, representation of a surface of an object (inanimate or living) in Three-dimensional space, three dimensions vi ...

. It appears in various 3D programs such as

Autodesk Maya Autodesk Maya, commonly shortened to just Maya (; ), is a 3D computer graphics application that runs on Windows, macOS, and Linux, originally developed by Alias and currently owned and developed by Autodesk. It is used to create assets for inter ...

Blender (software) Blender is a Free and open-source software, free and open-source 3D computer graphics software tool set that runs on Microsoft Windows, Windows, macOS, BSD, Haiku (operating system), Haiku, IRIX and Linux. It is used for creating animated films, ...

Cinema 4D Cinema 4D is a 3D software suite developed by the German company Maxon. Overview As of R21, only a single version of Cinema 4D is available. It replaces all previous variants, including BodyPaint 3D, and includes all features of the past 'Stu ...

. In most programs, it's referred to as an ico-spere, or

Icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...

. It is also commonly used as a dice in

Dungeons and Dragons ''Dungeons & Dragons'' (commonly abbreviated as ''D&D'' or ''DnD'') is a fantasy tabletop role-playing game (TTRPG) originally created and designed by Gary Gygax and Dave Arneson. The game was first published in 1974 by Tactical Studies Rule ...

External links

Conway Notation for Polyhedra
Try: "knAn", where n=4,5,6... example "k5A5" is an icosahedron. Bipyramids {{polyhedron-stub

Forms

Use

See also

External links