The Twisted Tetra consists of two parts which lock together with a twist to form a tetrahedron. The tetrahedron is one of two known polyhedra where each face shares a face with each other face.
The Szilassi polyhedron has seven hexagonal faces and is the only other known polyhedron where all faces are adjacent to all other faces. Hence seven colours are needed to colour the faces where no colour shares an edge with the same colour. The single hole makes this a torus or doughnut.
This is a double holed object and therefore has a genus-2 surface. However the surface is divided it requires a maximum of 8 colours to colour. Here the surface is divided in such a way to require eight colours.
2. Bobby’s Cube and Dodecahedron
Inspired by Robert Reid’s trisections of cubes our Bobby’s Cube twists apart simply enough but is tricky to get back together.
Following the same theme this dodecahedron has five identical pieces to twist together to form the solid.
A large level 4 Menger Sponge comes in two halves that shows off a beautiful star pattern on the sliced surface.
The Menger Bauble makes a unique Christmas tree decoration.