Look around the Graphics Lab

Regular, Semi-Regular Polyhedra, and thier Duals (first page)

Prisms, Anti-prisms, Pryamids, and related Polyhedra

Miscellanous Polyhedra: Deltahedra

Johnson Solids -- The other convex polyhedra with regular faces

Why I studied polyhedra, and Image Generation Techniques

Known Polyhedral Mathematical Formula

Data Sources and links for Polyhedral Data

Take two polygons and connect together with vertical edges of the same length to form squares. Each vertex has 3 edges, the new edge being at right angles to the edges of the original polygonal interface.The cylinder is a special 'infinite' case of this class.

This method is also known as elongation of the original polygons (See Johnson Solids).

Note: A "Square Prism" is more commonly known as a "Cube".

triangular_prism

off vrml

wikipedia

square_prism

off vrml

wikipedia

pentagonal_prism

off vrml

wikipedia

hexagonal_prism

off vrml

wikipedia

octagonal_prism

off vrml

wikipedia

decagonal_prism

off vrml

wikipedia

Join the polygons with triangles. each vertex will then have 4 edges, contecting the upper polygon with its lower polygon which is twisted slightly.The method of connecting is also known as gryo-elongation of the polygons. (See Johnson Solids).

Note: A "Triangular Antiprism" is also the platonic "Octahedron".

triangular_antiprism

off vrml

wikipedia

square_antiprism

off vrml

wikipedia

pentagonal_antiprism

off vrml

wikipedia

hexagonal_antiprism

off vrml

wikipedia

octagonal_antiprism

off vrml

wikipedia

decagonal_antiprism

off vrml

wikipedia

These may look like di-pyramids with unequal edge lengths but are much more specific. They are formed by taking the dual of a prism.As the number of edges of the original polygon increases, the pyramids become very long pointy.

The the "Square Di-pyramid" which also the a "Octahedron".

triangular_dipyramid

off vrml

wikipedia

square_dipyramid

off vrml

wikipedia

pentagonal_dipyramid

off vrml

wikipedia

hexagonal_bipyramid

off vrml

wikipedia

octagonal_bipyramid

off vrml

wikipedia

decagonal_bipyramid

off vrml

wikipedia

In a similar way these are the duals of a anti-prism. The faces are all kite shaped quadrilaterals, and like dual-prisms become very long as the number of faces increase.

The "Triangular Antiprism Dual" is also a "Cube".

triangular_trapezohedron

off vrml

wikipedia

square_trapezohedron

off vrml

wikipedia

pentagonal_trapezohedron

off vrml

wikipedia

hexagonal_trapezohedron

off vrml

wikipedia

octagonal_trapezohedron

off vrml

wikipedia

decagonal_trapezohedron

off vrml

wikipediaASIDE: the "Pentagonal Prism Dual" and "Pentagonal Antiprism Dual" are the only polyhedra that made a good ten-sided dice. The later is usually used as the points are better distributed, and are common in the paper and dice fantasy games such as "Advanced Dungeons and Dragons".

Basically forming a tent on a polygon. Note however that only three of these can be formed using edges of equal length, built using a triangle (forming a tetrahedron), a square (regular or square pyramid, like in Egypt), and a pentagon (or "pentagonal pyramid").If you try this with a hexagon, the object is flat, with six triangles on top of the hexagon, and no volume. After that it's impossible, unless you use longer edges to form the pyramid, but then the object will not conform to any standard polyhedral object.

In other words, there are only three true pyramid polyhedra...

Adding a pyramid to both sides of the original polygon will produce di-pryamids.

triangular_pyramid

off vrml

wikipedia

square_pyramid

off vrml

wikipedia

pentagonal_pyramid

off vrml

wikipediaThe "Triangular Pyramid" is a platonic "Tetrahedron", and the "Square Dipyramid" is a "Octohedron". The other four pyramidal solids form part the Johnson Solids Series (In sequence #1 #2 #12 and #13).

triangular_dipyramid

off vrml

wikipedia

square_dipyramid

off vrml

wikipedia

pentagonal_dipyramid

off vrml

wikipediaAside: Note that the famous Egyptian Pyramid does NOT conform to a regular square pyramid, but has angles which is thought to be of astronomical relevance, rather than mathematically.

These are gem like polygons which are formed by joining a polygon to another polygon with double the number of edges, using squares and triangles. Again only three such Cupolas exist.Bicupolas are like pyramids, just two of the objects joined back to back. In each case however they can be joined together in two different ways, ortho-bi-cupola, are mirrored across the join, and gryo-bi-cupola have a small twist so two triangles are not connected together by an edge.

triangular_cupola

off vrml

wikipedia

square_cupola

off vrml

wikipedia

pentagonal_cupola

off vrml

wikipedia

triangular_orthobicupola

off vrml

wikipedia

square_orthobicupola

off vrml

wikipedia

pentagonal_orthobicupola

off vrml

wikipediaThe "Triangular Gyrobicupola" is also the Archimedian Solid "Cuboctahedron", it is also the only object not part of the Johnson Solids (for the same reason).

triangular_gyrobicupola

off vrml

wikipedia

square_gyrobicupola

off vrml

wikipedia

pentagonal_gyrobicupola

off vrml

wikipedia

Created: 30 April 2001

Updated: 26 September 2003

Author: Anthony Thyssen, <Anthony.Thyssen@gmail.com>

URL:

`https://antofthy.gitlab.io/graphics/polyhedra/`