The scutoid (Nature, Gizmodo, New Scientist, eurekalert) is a newly defined shape found in epithelial cells. It's a 5-prism with a truncated vertex. The g6 format of the graph is KsP`?_HCoW?T .
They are apparently a building block for living creatures. One simple set of vertices that look reasonable with planar faces is {{2,4,0},{0,4,2},{0,2,4},{2,0,4},{4,0,2},{4,2,0},{1,3,6},{3,1,6},{6,6,2},{4,16,14}/3,{16,4,14}/3,{5,5,0}}.
What other mathematical properties do scutoids have? For example:
- Under what fixed parameters is the polyhedron a space-filler?
- If curved faces are allowed, are there more single-shape space-fillers?
- Is there a nice lattice representation with just a few different types of scutoid cells?
- What is the scutoid-building algorithm used by DNA?
Using code at Canonical Polyhedra, a canonical form looks like