# Polyprism Symmetries

A *polyprism*
is a solid formed by joining equal equilateral triangular prisms
at matching faces.
A polyprism
can have any of 32 forms of symmetry, including asymmetry.
Here are minimal examples of them.
Not all are uniquely minimal.
## 1-Fold Symmetry (Asymmetry)

This tetraprism has no symmetry.

## 2-Fold Symmetry

Polyprisms have 7 types of binary symmetry.

## 3-Fold Symmetry

Polyprisms may have one form of ternary symmetry,
generated by rotations on the vertical coordinate axis.

## 4-Fold Symmetry

Polyprisms have 7 types of quaternary symmetry.

## 6-Fold Symmetry

Polyprisms have 7 types of senary symmetry.

## 8-Fold Symmetry

Polyprisms have one form of octonary symmetry.

## 12-Fold Symmetry

Polyprisms have 7 types of duodenary symmetry.

## 24-Fold Symmetry

Polyprisms have one form of 24-fold symmetry.

Last revised 2020-07-18.

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Col. George Sicherman
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