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Wider Scope: List of Polyhedra by Type

Prism polyhedra are formed by stretching a polygon into three-dimensional space, or connecting two polygons with rectangles, or getting the Cartesian product of a polygon and a line segment (all three methods are identical). As there are an infinite number of uniform polygons, there are also an infinite number of prisms. Some significant prisms are, along with their Schläfli symbols:

• Henagonal Prism${\displaystyle \{\}\times \{1\}}$
• Digonal Prism${\displaystyle \{\}\times \{2\}}$
• Triangular Prism${\displaystyle \{\}\times \{3\}}$
• Cube${\displaystyle \{4,3\}}$
• Pentagonal Prism${\displaystyle \{\}\times \{5\}}$
• Hexagonal Prism${\displaystyle \{\}\times \{6\}}$
• Heptagonal Prism${\displaystyle \{\}\times \{7\}}$
• Octagonal Prism${\displaystyle \{\}\times \{8\}}$
• Enneagonal Prism${\displaystyle \{\}\times \{9\}}$
• Decagonal Prism${\displaystyle \{\}\times \{10\}}$
• Hendecagonal Prism${\displaystyle \{\}\times \{11\}}$
• Dodecagonal Prism${\displaystyle \{\}\times \{12\}}$
• Megagonal Prism${\displaystyle \{\}\times \{1000000\}}$
• Apeirogonal Prism${\displaystyle \{\}\times \{{\aleph }_{0}\}}$

## Henagonal Prism

A henagonal prism is a prism with a henagon as the base. Because of this, it is degenerate in normal Euclidean space.

It has the Schläfli symbol ${\displaystyle \{\}\times \{1\}}$, since it is the product of a line segment and a henagon.

### Hypervolumes

• vertex count = ${\displaystyle 2}$
• edge length = ${\displaystyle l}$
• surface area = ${\displaystyle 0{l}^{2}}$
• surcell volume = ${\displaystyle 0{l}^{3}}$

## Diagonal Prism

The digonal prism is a prism with a digon as the base. Because of this, it is degenerate in normal Euclidean space but in some geometries (such as spherical geometry) it can exist properly.

It has the Schläfli symbol ${\displaystyle \{\}\times \{2\}}$, since it is the product of a line segment and a digon. It also has the Schläfli symbol ${\displaystyle t\{2,2\}}$, since it is a truncated Digonal Dihedron and a truncated Digonal Hosohedron (both of which are in fact the same shape).

### Hypervolumes

• vertex count = ${\displaystyle 4}$
• edge length = ${\displaystyle 2 l}$
• surface area = ${\displaystyle 2{l}^{2}}$
• surcell volume = ${\displaystyle 0{l}^{3}}$

### Subfacets

Verticles Edges Faces Vertex Count Edges Length Surface Area
4 2 2 digons 4 ${\displaystyle 2 l}$ ${\displaystyle 2l^2}$

## Triangular Prism

A triangular prism is a prism with a triangle as its base. It is the simplest non-degenerate prism in Euclidean geometry.

Verticles Edges Faces Cells Vertex Count Edges Length Surface Area Surcell Volume
6 9 2 triangles 1 triangular prism 6 ${\displaystyle 9 l}$ ${\displaystyle {\frac {{\sqrt {3}}+6}{2}}l^{2}}$ ${\displaystyle \frac{\sqrt{3}}{4} l^3}$

## Square Prism

A square prism is a three-dimensional shape. True to its name, it has a square base and four triangular faces meeting at an apex and each with one side sharing an edge with the object's base.

## Pentagonal Prism

A pentagonal prism is a prism with a pentagon as its base.

Verticles Edges Faces Cells Vertex Count Edges Length Surface Area Surcell Volume
10 15 2 pentagons 1 pentagonal prism 10 ${\displaystyle 15l}$ ${\displaystyle {\frac {10+{\sqrt {5(5+2{\sqrt {5}})}}}{2}}{l}^{2}}$ ${\displaystyle {\frac {\sqrt {5(5+2{\sqrt {5}})}}{4}}{l}^{3}}$

## Prism Polyhedron Subfacets

X = Sides of Base