Morphing the Császár Polyhedron

morph polyhedra

symmetry axis
opacity
faces
{5, 1, 6}, {6, 1, 2}
{5 ,7, 1}, {6, 2, 7}
{4, 6, 7}, {7, 3, 1}
{4, 7, 5}, {7, 2, 3}
{2, 4, 5}, {2, 5, 3}
{1, 4, 2}, {3, 5, 6}
{1, 3, 4}, {3, 6, 4}
Hamiltonian cycles
H{1, 2, 3, 4, 5, 6, 7}
H{1, 3, 5, 7, 2, 4, 6}
H{1, 4, 7, 3, 6, 2, 5}

Cs0: Csaszar, 1949

Four versions of the Császár polyhedron are shown. You can study the transition between these versions. In each of the four, the triangles shared by adjacent tetrahedra form a Möbius band. Each Möbius band contains all seven vertices of the Császár polyhedron, but only 14 of its edges. The edges of the Möbius graph form three Hamiltonian cycles, which are exactly loops, if the faces of the polyhedron do not intersect one another. If the faces intersect one another and the edges do not intersect one another, then one of the Hamiltonian cycles might not form a loop.