# Truncated dodecagonal duoprism

Truncated dodecagonal duoprism
Rank4
TypeIsogonal
Notation
Elements
Cells144 tetragonal disphenoids, 24 truncated dodecagonal prisms
Faces576 isosceles triangles, 144 ditetragons, 24 didodecagons
Edges288+288+576
Vertices576
Vertex figureSphenoid
Measures (based on icositetragon edge length 1)
Edge lengthsLacing edges (576): ${\displaystyle {\sqrt {3}}-1\approx 0.73205}$
Edges of icositetragons (288+288): 1
Circumradius${\displaystyle {\sqrt {\frac {20+9{\sqrt {2}}+6{\sqrt {3}}+7{\sqrt {6}}}{2}}}\approx 5.48938}$
Central density1
Related polytopes
DualTetrakis dodecagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)≀S2, order 1152
ConvexYes
NatureTame

The truncated dodecagonal duoprism or tatwaddip is a convex isogonal polychoron that consists of 24 truncated dodecagonal prisms and 144 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated dodecagonal prisms join at each vertex. It can be formed by truncating the dodecagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform dodecagonal-icositetragonal duoprisms chosen such that the icositetragonal and dodecagonal prisms have the same circumradius. if the icositetragons of this duoprism have edge length 1, the dodecagons have edge length ${\displaystyle 1-{\sqrt {2}}+{\sqrt {6}}\approx 2.03528}$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle {\frac {1+{\sqrt {3}}}{2}}}$ ≈ 1:1.36603.