The dodecagonal duoprism or twaddip, also known as the dodecagonal-dodecagonal duoprism, the 12 duoprism or the 12-12 duoprism, is a noble uniform duoprism that consists of 24 dodecagonal prisms, with 4 joining at each vertex. It is also the 24-11 gyrochoron. It is the first in an infinite family of isogonal dodecagonal dihedral swirlchora and also the first in an infinite family of isochoric dodecagonal hosohedral swirlchora.
|Bowers style acronym||Twaddip|
|Coxeter diagram||x12o x12o ()|
|Cells||24 dodecagonal prisms|
|Faces||144 squares, 24 dodecagons|
|Vertex figure||Tetragonal disphenoid, edge lengths (√2+√6)/2 (bases) and √2 (sides)|
|Measures (edge length 1)|
|Dichoral angles||Twip–12–twip: 150°|
|Number of external pieces||24|
|Level of complexity||3|
|Abstract & topological properties|
|Symmetry||I2(12)≀S2, order 1152|
This polychoron can be alternated into a hexagonal duoantiprism, although it cannot be made uniform. Twelve of the dodecagons can also be alternated into long ditrigons to create a hexagonal-hexagonal prismantiprismoid, or it can be subsymmetrically faceted into a square triswirlprism or a triangular tetraswirlprism, which are nonuniform.
The vertices of a dodecagonal duoprism of edge length 1, centered at the origin, are given by:
A dodecagonal duoprism has the following Coxeter diagrams:
- x12o x12o (full symmetry)
- x6x x12o (one dodecagon as dihexagon)
- x6x x6x (both dodecagons as dihexagons)
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "twaddip".