Toroidal blend of 6 hexagonal prisms

Toroidal blend of 6 hexagonal prisms
(3D model) (OFF file)
Rank	3
Type	Stewart toroid
Notation
Stewart notation	P6P6P6P6P6P6
Elements
Faces	3+3+6 hexagons, 6+6+12 squares
Edges	3+3+6+6+6+12+12+12+12+12
Vertices	6+6+6+6+12+12
Measures (edge length 1)
Volume	$9{\sqrt {3}}\approx 15.58846$
Surface area	$24+18{\sqrt {3}}\approx 55.17691$
Central density	0
Abstract & topological properties
Flag count	336
Euler characteristic	0
Surface	Torus
Orientable	Yes
Genus	1
Properties
Symmetry	A2×A1, order 6
Convex	No

The toroidal blend of 6 hexagonal prisms is a Stewart toroid. It is an outer-blend of 6 hexagonal prisms. It is the smallest Stewart toroid which can be made by blending hexagonal prisms. The blend of 2 hexagonal prisms is a smaller toroid made from blending hexagonal prisms, but its faces intersect disqualifying it from being a Stewart toroid.

Vertex coordinates

The coordinates of a toroidal blend of 6 hexagonal prisms, centered at the origin and with unit edge length, are:

• $\left(0,\,3,\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,{\frac {5}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,{\frac {3}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {3{\sqrt {3}}}{4}},\,{\frac {3}{4}},\,\pm 1\right),$
• $\left(\pm {\sqrt {3}},\,0,\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {3{\sqrt {3}}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {3{\sqrt {3}}}{2}},\,-{\frac {3}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\sqrt {3}},\,-2,\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,-{\frac {3}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(0,\,-{\frac {3}{2}},\,\pm 1\right),$
• $\left(0,\,1,\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{4}},\,{\frac {1}{4}},\,\pm 1\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(0,\,-{\frac {1}{2}},\,\pm 1\right).$