Cameron Strachan

activity

20202026

collaborators

6 papers

math.CO2026

The number of touching pairs of congruent sphere packings in Euclidean 3-space

Cameron Strachan

A packing of $n$ congruent balls in $R^{3}$ is a family of interior-disjoint Euclidean balls all having the same radius. The contact number of a packing is the number of tou…

math.CO2025

Edge isoperimetry of lattices

Cameron Strachan, Konrad Swanepoel

We present two results related to an edge-isoperimetric question for Cayley graphs on the integer lattice asked by Ben Barber and Joshua Erde [Isoperimetry of Integer Lattices, Dis…

math.CO2022

Vertex Classification of Planar C-polygons

Illya Ivanov, Cameron Strachan

Given a convex domain $C$ , a $C$ -polygon is an intersection of $n \geq 2$ homothets of $C$ . If the homothets are translates of $C$ then we call the intersection a translative $C$ -po…

math.GT2022

The Number of Singularities in the Intersections of Convex Planar Translates

Cameron Strachan

This purpose of this paper is to prove the following result: let phi be a strictly convex, smooth, convex body in the Euclidean plane, if the intersection of n translates of phi ha…

math.MG2022

Illuminating spiky balls and cap bodies

Károly Bezdek, Ilya Ivanov, Cameron Strachan

The convex hull of a ball with an exterior point is called a spike (or cap). A union of finitely many spikes of a ball is called a spiky ball. If a spiky ball is convex, then we ca…

math.MG2020

On the illumination of centrally symmetric cap bodies in small dimensions

Ilya Ivanov, Cameron Strachan

The illumination number $I (K)$ of a convex body $K$ in Euclidean space $E^{d}$ is the smallest number of directions that completely illuminate the boundary of a convex body.…