# Compound of three triangular prisms

Compound of three triangular prisms
Rank3
TypeUniform
Elements
Components3 triangular prisms
Faces9 squares, 6 triangles as 3 fissal enneagrams
Edges9+18
Vertices18
Vertex figureIsosceles triangle, edge lengths 1, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {21}}{6}}\approx 0.76376}$
Volume${\displaystyle {\frac {3{\sqrt {3}}}{4}}\approx 1.29904}$
Dihedral angles4–3: 90°
4–4: 60°
Height1
Central density3
Number of external pieces20
Level of complexity6
Related polytopes
ArmySemi-uniform Ep, edge lengths ${\displaystyle {\frac {2{\sqrt {3}}\sin \pi 9}{3}}}$ (base), 1 (sides)
Regiment*
DualCompound of three triangular tegums
ConjugateCompound of three triangular prisms
Abstract & topological properties
Flag count108
OrientableYes
Properties
SymmetryI2(9)×A1, order 36
ConvexNo
NatureTame

The fissal enneagrammic prism or compound of three triangular prisms is a prismatic uniform polyhedron compound. It consists of 2 fissal enneagrams and 9 squares. Each vertex joins one fissal enneagram and two squares. As the name suggests, it is a prism based on a fissal enneagram.

Its quotientprismatic equivalent is the 9-3 step prismatic prism, which is five-dimensional.

## Vertex coordinates

Coordinates for the vertices of a fissal enneagrammic prism of edge length 1 centered at the origin are given by:

• ${\displaystyle \left({\frac {\sqrt {3}}{3}},\,0,\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {2\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {2\pi }{9}}}{3}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {4\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {4\pi }{9}}}{3}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left({\frac {{\sqrt {3}}\cos {\frac {8\pi }{9}}}{3}},\,\pm {\frac {{\sqrt {3}}\sin {\frac {8\pi }{9}}}{3}},\,\pm {\frac {1}{2}}\right).}$