Matthew Ellison

activity

20232026

collaborators

4 papers

math.MG2026

Neoplatonic solids

Peter Doyle, Matthew Ellison

A \emph{6-net} is a simplicial triangulation of the $2$ -sphere with maximum degree $\leq 6$ . Experiments suggest that every $6$ -net admits a unique realization as an undented Eucli…

math.GT2025

Taut fillings

Peter Doyle, Matthew Ellison, Zili Wang

Let $σ$ be a simplicial triangulation of the 2-sphere, $X$ the associated integral 2-cycle. A filling of $X$ is an integral 3-chain $M$ with $\partial M = X$ ; a taut filling is one…

math.AT2024

Lower bounds and integrality gaps in simplicial decomposition

Matthew Ellison

Let $K$ be a finite pure simplicial $d$ -complex, with oriented facets ${F_{i}}$ , which is boundaryless in the sense that $\sum \partial F_{i} = 0$ . We call such a $\mathcal{K}…

math.GT2023

Realizing abstract simplicial complexes with specified edge lengths

Matthew Ellison

For finite abstract simplicial complex $Σ$ , initial realization $α$ in $E^{d}$ , and desired edge lengths $L$ , we give practical sufficient conditions for the existence of a…