Catalan solids

thingiverse

Catalan Solids Make Perfect Dice Due to Face-Transitive Design These three-dimensional figures are formed by taking duals of the Archimedean solids and are uniquely characterized as being face-transitive. Inherently fair dice can be produced with them, thanks to their geometry. Important Details - Rafts: All models should have raft support. - Supports: - A necessity for all Catalan solids. Note All models except the rhombic dodecahedron are required to use supports in order to maintain integrity during the printing process. Orientation may vary as each model has been set according to its closest possible symmetry with a cubic shape, although not one is fully cubic due to various irregularities. In particular, several of the figures will require rotations prior to 3D printing in order to achieve correct positioning. Background Each of these models was originally created using TinkerCad as an aid for educational purposes. Further enhancements were required for accurate reproduction of complex solids with unique orientations which were difficult to replicate in 1-degree increments that the tool limits its accuracy. In turn, it sparked a desire to generate shapes on-demand and prompted further refinement through developing algorithms capable of creating three-dimensional models by superimposing layers and manipulating work planes according to set coordinates to get precise angles up to a tenth of one degree or more for some pieces where higher detail may be crucial, thereby producing high-precision dice that are always accurate