|Bowers style acronym||Tisdip|
|Coxeter diagram||x3o x4o ()|
|Cells||4 triangular prisms, 3 cubes|
|Faces||4 triangles, 3+12 squares|
|Vertex figure||Digonal disphenoid, edge lengths 1 (base 1) and √ (base 2 and sides)|
|Measures (edge length 1)|
|Dichoral angles||Trip–4–cube: 90°|
|Heights||Square atop cube:|
|Trip atop trip: 1|
|Number of external pieces||7|
|Level of complexity||6|
|Abstract & topological properties|
|Symmetry||A2×B2, order 48|
The triangular-square duoprism or tisdip, also known as the 3-4 duoprism, is a uniform duoprism that consists of 3 cubes and 4 triangular prisms, with two of each meeting at each vertex. It can also be seen as a prism based on the triangular prism, which makes it a convex segmentochoron (designated K-4.18 on Richard Klitzing's list) in two different ways, as a prism of a triangular prism or square atop cube.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a triangular-square duoprism of edge length 1, centered at the origin, are given by:
Representations[edit | edit source]
A triangular-square duoprism has the following Coxeter diagrams:
- x3o x4o (full symmetry)
- x x x3o (A2×A1×A1 symmetry, triangular prismatic prism)
- xx xx3oo&#x (A2×A1 axial, prism of triangular prism)
- ox xx4oo&#x (BC2×A1 axial, square atop cube)
- ox xx xx&#x (A1×A1×A1 symmetry, as above with rectangles instead of squares)
- xxx3ooo oqo&#xt (A2×A1 axial, triangle-first)
- xxx xxx&#x (A1×A1 symmetry, 3 squares seen separately)
[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "tisdip".
- Quickfur. "The 3,4-Duoprism".
- Wikipedia contributors. "3-4 duoprism".