ANPA Conference · Cambridge University · August 2020
Original Geometric Polyhedra Research — Mereon Matrix
Co-discovered a novel family of geometric polyhedra with properties unseen in existing literature. Presented findings at the ANPA Conference at Cambridge University in August 2020 — an invitation that followed solving a 20-year-old geometric problem in under four hours. Collaborated with Dr. Lou Kauffman (University of Illinois Chicago) and Dr. Robert Grey on advanced topological geometry. Led the undergraduate research team at UCCS under Dr. Alexander Soifer.
Novel polyhedraMereon MatrixTopological geometryCambridge
Collaborators
Dr. Lou Kauffman, Dr. Robert Grey
Supervisor
Dr. Alexander Soifer, UCCS
Problem solved
20-year open problem in under 4 hours
01 — Combinatorics
Hadwiger-Nelson Problem
Computational pipeline building a taxonomy of unit-distance graphs in Q(√3, √11). Mechanistic explanation of de Grey's 2018 construction. Combinatorial impossibility proofs.
χ_f = 7/2 found consistently as algebraic invariant across all tested graph families
02 — Dimensional Geometry
Hyperdimensional Visualization 3D–6D
Theoretical framework for hyperdimensional mathematical visualization spanning 3D through 6D polytope systems. UE5 implementation with hypercube actors at each dimensional level. Golden ratio spiral generators and dimensional transformation animations.
GoldenRatio UE5 project: live hypercube actors spanning all dimensions simultaneously
03 — Acoustic Geometry
Geometric Cymatics
Independently discovered geometry family linking acoustic phenomena to 3D form through rotational transformation. Dodecahedron series designated Level 1 of the Geometric Cymatics Evolution framework. Rhombic triacontahedron tessellations applicable to simulation validation.
Geometric Cymatics Evolution: a structured taxonomy of form emerging from frequency