|Bowers style acronym||Dedip|
|Coxeter diagram||x10o x10o ()|
|Cells||20 decagonal prisms|
|Faces||100 squares, 20 decagons|
|Vertex figure||Tetragonal disphenoid, edge lengths √(5+√5)/2 (bases) and √2 (sides)|
|Measures (edge length 1)|
|Dichoral angles||Dip–10–dip: 144º|
|Number of external pieces||20|
|Level of complexity||3|
|Abstract & topological properties|
|Symmetry||I2(10)≀S2, order 800|
The decagonal duoprism or dedip, also known as the decagonal-decagonal duoprism, the 10 duoprism or the 10-10 duoprism, is a noble uniform duoprism that consists of 20 decagonal prisms, with four at each vertex. It is also the 20-9 gyrochoron. It is the first in an infinite family of isogonal decagonal dihedral swirlchora and also the first in an infinite family of isochoric decagonal hosohedral swirlchora.
This polychoron can be alternated into a pentagonal duoantiprism, although it cannot be made uniform.
A unit decagonal duoprism can be edge-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.
Gallery[edit | edit source]
Wireframe, cell, net
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a decagonal duoprism of edge length 1, centered at the origin, are given by:
Representations[edit | edit source]
A decagonal duoprism has the following Coxeter diagrams:
- x10o x10o (full symmetry)
- x5x x10o (one decagon as dipentagon)
- x5x x5x (both decagons have pentagonal symmetry)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
- Klitzing, Richard. "dadip".
- Wikipedia Contributors. "10-10 duoprism".