## Acute triangulations of polyhedra in Rn

### Eryk Kopczyński, Igor Pak & Piotr Przytycki

From this webpage you can download the computer programs used to create the acute triangulation of the cube and the dodecahedron, mentioned in the paper. You can also use these programs to view and animate the triangulation.
You can download the package here. It contains two programs, CUBE and CELL. For each of the two programs, source code and a Microsoft Windows executable is included. Source code compiles under MS Windows (using MinGW + SDL) and under Linux.

CELL can be used to view the triangulation of the regular tetrahedron, animate the algorithms used to triangulate the rectangular tetrahedron and the regular dodecahedron, and to generate the files cube.dat (which describes the triangulation of the cube) and dodeca.dat (which describes the triangulation of the dodecahedron). It can also be used for experimentation.

CUBE reads the cube.dat file containing an acute triangulation of the cube, verifies it, and animates it on the screen.
Both programs are controlled with keyboard. You can press the following keys:

 q quit arrows,PgUp,PgDn rotate the picture Home hold Home while rotating to rotate slower CUBE only: z,x zoom in/out 6 export the picture to SVG 8 export the picture to SVG; only the skeleton CELL only: u,i,o,p change which vertices are shown (by vertex types) t select all vertices shown z,x move all the selected vertices towards/outwards the center (this means zoom in/out if all vertices are selected) v verify the current structure (see the comment below) s show only incorrect edges (red and green ones) r animate the flattening algorithm (used to triangulate the rectangular tetrahedron) c run/animate the flattening algorithm for the dodecahedron triangulation; save the result to dodeca.dat b use the result from dodeca.dat file instead of running the algorithm d stop the display (makes the flattening algorithm faster) . generate the cube.dat file

Verification paints each edge with a color which corresponds to its status. Edges with no errors found are painted white. For each tetrahedron ABCD, if the dihedral angle at edge AB is not acute, AB is painted red, and edges AC,AD,BC,BD are painted green (unless already red).