|Faces||2+2 asymmetric triangles, 2+2 parallelograms|
|Abstract & topological properties|
|Symmetry||K2+×I, order 2|
Solution to the einstein problem[edit | edit source]
The Schmitt–Conway–Danzer biprism can be made to tessellate 3-dimensional space and no tiling of just Schmitt–Conway–Danzer biprisms has any translational symmetry. However, some of these tilings have screw symmetry, that is symmetries which are a simultaneous rotation and translation. These tilings are thus aperiodic but not strongly aperiodic. This makes the Schmitt–Conway–Danzer biprism a solution to some versions of the einstein problem, which do not require the strong version of aperiodicity.
The Schmitt–Conway–Danzer biprism along with its mirror image can tile the plane periodically.
History[edit | edit source]
A non-convex variant was originally discovered by Schmitt in 1998. Schmitt conjectured that it could be made convex while maintaining its properties as a prototile. Conway found such a variant and in 1993 Danzer improved the design further.
[edit | edit source]
- Weisstein, Eric W. "Schmitt-Conway Biprism" at MathWorld.