4 problems

Hougardy–Lutz–Zelke realizability conjecture for triangulated orientable surfaces
Hougardy–Lutz–Zelke conjecture. Every triangulation of an orientable surface of genus $g$ with
openFrom papersgeometric-realization surface-topology triangulations
0 responses
8
Duke's realization conjecture for triangulated tori
Duke's torus-realization conjecture. Every triangulated torus can be realized as a polyhedron in $\mathbb{R}^3$ .
openFrom papersgeometric-realization tori triangulated-surfaces
0 responses
3
Geometric realization conjecture for path triangulations in digital images
A path triangulation is a triangulation obtained from paths in a planar cell complex, and a triangulated digital image is a digital image equipped with such a triangulation. Geomet…
openFrom papersdigital-topology geometric-realization triangulations
0 responses
6
The geometric realization conjecture for triangulated closed orientable surfaces of genus at most four
Geometric realization conjecture. Every triangulation of a closed orientable surface of genus at most $4$ is realizable in $\mathbb{R}^3$ by straight edges, flat triangles, and wit…
openFrom papersgeometric-realization topological-graph-theory triangulated-surfaces
0 responses
5

Hougardy–Lutz–Zelke realizability conjecture for triangulated orientable surfaces