Octagrammic antiprism

Octagrammic antiprism
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Stoap
Coxeter diagram	s2s16/3o
Elements
Faces	16 triangles, 2 octagrams
Edges	16+16
Vertices	16
Vertex figure	Isosceles trapezoid, edge lengths 1, 1, 1, √2–√2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {6-2{\sqrt {2}}+{\sqrt {20-14{\sqrt {2}}}}}{8}}}\approx 0.67267$
Volume	${\frac {2{\sqrt {4-2{\sqrt {2}}+2{\sqrt {146-103{\sqrt {2}}}}}}}{3}}\approx 1.01782$
Dihedral angles	8/3–3: $\arccos \left(-{\sqrt {\frac {7-4{\sqrt {2}}+2{\sqrt {20-14{\sqrt {2}}}}}{3}}}\right)\approx 112.69174^{\circ }$
	3–3: $\arccos \left({\frac {1-2{\sqrt {2-{\sqrt {2}}}}}{3}}\right)\approx 100.18990^{\circ }$
Height	${\sqrt {\frac {-2+2{\sqrt {2}}+{\sqrt {20-14{\sqrt {2}}}}}{2}}}\approx 0.79899$
Central density	3
Number of external pieces	82
Level of complexity	24
Related polytopes
Army	Non-uniform Oap, edge lengths ${\sqrt {2}}-1$ (base), ${\sqrt {1-{\sqrt {10-7{\sqrt {2}}}}}}$ (sides)
Regiment	Stoap
Dual	Octagrammic antitegum
Conjugates	Octagonal antiprism, Octagrammic retroprism
Convex core	Octagonal antibifrustum
Abstract & topological properties
Flag count	128
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	(I2(16)×A1)/2, order 32
Convex	No
Nature	Tame

The octagrammic antiprism, or stoap, is a prismatic uniform polyhedron. It consists of 16 triangles and 2 octagrams. Each vertex joins one octagram and three triangles. As the name suggests, it is an antiprism based on an octagram. It is one of two octagrammic antiprisms, the other one being the octagrammic retroprism.

Vertex coordinates

An octagrammic antiprism of edge length 1 has vertex coordinates given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,H\right),$
• $\left(\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,H\right),$
• $\left(0,\,\pm {\sqrt {\frac {2-{\sqrt {2}}}{2}}},\,-H\right),$
• $\left(\pm {\sqrt {\frac {2-{\sqrt {2}}}{2}}},\,0,\,-H\right),$
• $\left(\pm {\frac {\sqrt {2-{\sqrt {2}}}}{2}},\,\pm {\frac {\sqrt {2-{\sqrt {2}}}}{2}},\,-H\right),$

where $H={\sqrt {\frac {-2+2{\sqrt {2}}+{\sqrt {20-14{\sqrt {2}}}}}{8}}}$ is the distance between the antiprism's center and the center of one of its bases.

External links

• Wikipedia contributors. "Octagrammic antiprism".
• McCooey, David. "Octagrammic Antiprism"