3 papers
math.GT2024
Oriented and Non-oriented Cubical Surfaces in The Penteract
Manuel Estevez, Erika Roldan, Henry Segerman
Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldan, show tha…
math.GT2023
Surfaces in The Tesseract
Manuel Estévez, Erika Roldan, Henry Segerman
How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Roldán showed that the torus and the sphere are the only cl…
math.CO2022
Parity Property of Hexagonal Sliding Puzzles
Ray Karpman, Erika Roldan
We study the puzzle graphs of hexagonal sliding puzzles of various shapes and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvabilit…