|Bowers style acronym||Twip|
|Coxeter diagram||x x12o ()|
|Faces||12 squares, 2 dodecagons|
|Vertex figure||Isosceles triangle, edge lengths √2, √2, √2+√3|
|Measures (edge length 1)|
|Dihedral angles||4–4: 150°|
|Number of pieces||14|
|Level of complexity||3|
|Symmetry||I2(12)×A1, order 48|
The dodecagonal prism, or twip, is a prismatic uniform polyhedron. It consists of 2 dodecagons and 12 squares. Each vertex joins one dodecagon and two squares. As the name suggests, it is a prism based on a dodecagon.
Vertex coordinates[edit | edit source]
A dodecagonal prism of edge length 1 has vertex coordinates given by:
Representations[edit | edit source]
A dodecagonal prism has the following Coxeter diagrams:
- x x12o (full symmetry)
- x x6x (generally a dihexagonal prism)
- s2s12x (generally a dihexagonal trapezoprism)
- xx12oo&#x (bases esen separately)
Semi-uniform variant[edit | edit source]
The dodecagonal prism has a semi-uniform variant of the form x y12o that maintains its full symmetry. This variant uses rectangles as its sides.
With base edges of length a and side edges of length b, its circumradius is given by and its volume is given by .
A decagonal prism with base edges of length a and side edges of length b can be alternated to form a hexagonal antiprism with base edges of length and side edges of lengths . In particular if the side edges are times the length of the base edges this gives a uniform pentagonal antiprism.
Variations[edit | edit source]
A dodecagonal prism has the following variations:
- Dihexagonal prism - prism with dipentagons as bases, and 2 types of rectangles
- Dihexagonal trapezoprism - isogonal with trapezoid sides
- Dodecagonal frustum
- dihexagonal frustum
External links[edit | edit source]
- Klitzing, Richard. "twip".
- Wikipedia Contributors. "Dodecagonal prism".