Enneagonal disphenoid

Enneagonal disphenoid
(OFF file)
Rank	5
Type	Noble
Notation
Bowers style acronym	Edow
Elements
Tera	18 enneagonal scalenes
Cells	81 tetragonal disphenoids, 18 enneagonal pyramids
Faces	162 isosceles triangles, 2 enneagons
Edges	18+81
Vertices	18
Vertex figure	Enneagonal scalene
Measures (base edge length 1, height h)
Edge lengths	Edges of base enneagons (18): 1
	Lacing edges (81): ${\sqrt {{\frac {1}{2\sin ^{2}{\frac {\pi }{9}}}}+h^{2}}}$
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{9}}}}+{\frac {h^{2}}{4}}}}$
Central density	1
Related polytopes
Army	Edow
Regiment	Edow
Dual	Enneagonal disphenoid
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(9)▲S2, order 648
Convex	Yes
Nature	Tame

The enneagonal disphenoid or edow is a convex noble polyteron with 18 enneagonal scalenes as facets. 11 facets join at each vertex. However, it cannot be made scaliform, because the length of the lacing edges must be greater than the base edges.