TITLE: Has anyone discovered a convex space-filling 15-faced polyhedron?
QUESTION [6 upvotes]: 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 that "no one has found a 15 faced space-filler, nor has anyone proved its nonexistence". 
I realize that several might have been found since then, but i have no way of verifying it, or checking which types has then been found.

REPLY [3 votes]: Yes.
Vertex coordinates:
0 0.293715 0.406952;
0 0.57735 0.225;
0 0.57735 0.462844;
0.141706 -0.0818139 0.490403;
0.173205 0.67735 0.675;
0.326795 -0.188675 0.675;
0.358294 0.370489 -0.0404031;
0.358294 0.570489 0.859597;
0.358294 0.784212 0.490403;
0.5 -0.0050396 0.0430477;
0.5 -0.0886751 0.887156;
0.5 -0.288675 0.225;
0.5 -0.288675 0.462844;
0.5 0.19496 0.943048;
0.641706 0.370489 -0.0404031;
0.641706 0.570489 0.859597;
0.641706 0.784212 0.490403;
0.673205 -0.188675 0.675;
0.826795 0.67735 0.675;
0.858294 -0.0818139 0.490403;
1 0.293715 0.406952;
1 0.57735 0.225;
1 0.57735 0.462844.
This is the only one I am aware of. I made it in voro++ by taking the Voronoi partition of a set of 2 points within an 'almost' hexagonal periodic box.