Truncated octagonal duoprism

Truncated octagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Trodip
Elements
Cells	64 tetragonal disphenoids, 16 truncated octagonal prisms
Faces	256 isosceles triangles, 64 ditetragons, 16 dioctagons
Edges	128+128+256
Vertices	256
Vertex figure	Sphenoid
Measures (variant with hexadecagon edge length 1)
Edge lengths	Lacing edges (256): ${\sqrt {2-{\sqrt {2}}}}\approx 0.76537$
	Edges of hexadecagons (128+128): 1
Circumradius	${\sqrt {\frac {10+3{\sqrt {2}}+{\sqrt {100+62{\sqrt {2}}}}}{2}}}\approx 3.73780$
Central density	1
Related polytopes
Army	Trodip
Regiment	Trodip
Dual	Tetrakis octagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)≀S2, order 512
Convex	Yes
Nature	Tame

The truncated octagonal duoprism or trodip is a convex isogonal polychoron that consists of 16 truncated octagonal prisms and 64 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated octagonal duoprisms join at each vertex. It can be formed by truncating the octagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform octagonal-hexadecagonal duoprisms chosen such that the hexadecagonal and octagonal prisms have the same circumradius. if the hexadecagons of this duoprism have edge length 1, the octagons have edge length $1+{\sqrt {4-2{\sqrt {2}}}}\approx 2.08239$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\sqrt {\frac {2+{\sqrt {2}}}{2}}}$ ≈ 1:1.30656.