Tetrapod

Tetrapod
Rank2
TypeSemi-uniform
Notation
Bowers style acronymTepod
Coxeter diagramx4/3y
Elements
Edges4+4
Vertices8
Measures (edge lengths a , b )
Circumradius${\displaystyle {\sqrt {\frac {a^{2}+b^{2}-ab{\sqrt {2}}}{2}}}}$
Angle45°
Related polytopes
ArmyDiteg
DualConcave tetrambus
Abstract & topological properties
Flag count16
OrientableYes
Properties
SymmetryB2, order 8
ConvexNo
NatureTame

The tetrapod is a semi-uniform polygon that has 8 sides of two different edge lengths. The angles of a tetrapod are always 45 degrees. It is a faceting of the ditetragon.

A tetrapod generally has the Coxeter diagram x4/3y, where the ratio between the two edge classes is greater than ${\displaystyle {\sqrt {2}}}$. If the ratio is less than this value, another semi-uniform polygon called the ditetragram results. If the edge ratio is exactly ${\displaystyle {\sqrt {2}}}$, the polygon degenerates into something that looks like a square with its diagonals drawn in, except that each diagonal edge is double-covered.

Vertex coordinates

A tetrapod with minor edge length 1 and major edge length x centered at the origin will have vertex coordinates given by all permutations of:

• ${\displaystyle (\pm ({\frac {x^{2}}{2}}+{\frac {1}{4}}),\pm {\frac {1}{2}})}$