Dodecagonal duoexpandoprism

Dodecagonal duoexpandoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Twaddep
Coxeter diagram	xo12xx ox12xx&#zy
Elements
Cells	144 tetragonal disphenoids, 288 wedges, 144 rectangular trapezoprisms, 24+24 dodecagonal prisms
Faces	576 isosceles triangles, 576 isosceles trapezoids, 288+288 rectangles, 48 dodecagons
Edges	288+288+576+576
Vertices	576
Vertex figure	Mirror-symmetric triangular antiprism
Measures (based on two dodecagonal-icositetragonal duoprisms of edge length 1)
Edge lengths	Edges of duoprisms (288+288+576): 1
	Lacing edges (576): $1+{\sqrt {3}}\approx 2.73205$
Circumradius	${\sqrt {6+3{\sqrt {3}}+{\sqrt {26+15{\sqrt {3}}}}}}\approx 4.29012$
Central density	1
Related polytopes
Army	Twaddep
Regiment	Twaddep
Dual	Dodecagonal duoexpandotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	Yes
Nature	Tame

The dodecagonal duoexpandoprism or twaddep is a convex isogonal polychoron and the eleventh member of the duoexpandoprism family. It consists of 48 dodecagonal prisms of two kinds, 144 rectangular trapezoprisms, 288 wedges, and 144 tetragonal disphenoids. 2 dodecagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal dodecagonal-icositetragonal duoprisms, or more generaly dodecagonal-didodecagonal duoprisms, and a subset of its variations can be formed by expanding the cells of the dodecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {2}{1+{\sqrt {2{\sqrt {78+45{\sqrt {3}}}}-8{\sqrt {3}}-11}}}}$ ≈ 1:1.48709.