Matthias Schwar
Hamiltonian Dodecahedron and its 3 cycles
The basic edge dodecahedron was designed by Ryosuke Sakurai.
For this model I used a peculiar colour pattern: a Hamiltonian Cycle, a loop touching each vertex exactly once. There is only one possible way to achieve this, however there are 60 different 2D projections (12 pentagonal faces, each has 5 sides). Most of them can be aligned by rotation, except 3. Based on their appearance, I call them "Spiral", "Rabbit" and "Reader".
The Hamiltonian Dodecahedron is chiral, there are two forms which are mirror images of each other.
I found this distinct patterns when i was trying to figure out a way how to color origami models with dodecahedral/icosahedral geometry in 3 colours, different colours at every 3-point-center.
Hamiltonian Dodecahedron and its 3 cycles
The basic edge dodecahedron was designed by Ryosuke Sakurai.
For this model I used a peculiar colour pattern: a Hamiltonian Cycle, a loop touching each vertex exactly once. There is only one possible way to achieve this, however there are 60 different 2D projections (12 pentagonal faces, each has 5 sides). Most of them can be aligned by rotation, except 3. Based on their appearance, I call them "Spiral", "Rabbit" and "Reader".
The Hamiltonian Dodecahedron is chiral, there are two forms which are mirror images of each other.
I found this distinct patterns when i was trying to figure out a way how to color origami models with dodecahedral/icosahedral geometry in 3 colours, different colours at every 3-point-center.