1
vote
2answers
34 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
4
votes
2answers
152 views

Has anyone discovered a convex space-filling 15-faced polyhedron?

I've been looking for extensive surveys regarding space-filling polyhedra, but have only come across Michael Goldbergs "Convex polyhedral space-fillers of more than twelve faces" from 1979, stating ...
12
votes
1answer
530 views

Floret Tessellation of a Sphere

I'm a programmer looking to create a 3D model of a Floret Tessellation of a sphere, like the one in this picture Class III 8,11 floret planar net (source) If anyone could point me in the right ...
1
vote
1answer
167 views

Are there formulae to determine close-packing polyhedra?

Is there a formula to determine which polyhedra will tessellate in 3D without any spaces?