On non-isomorphic biminimal pots realizing the cube

TL;DR

This paper disproves a recent conjecture by providing explicit examples of minimal biminimal pots that realize the cube, demonstrating their uniqueness up to isomorphism.

Contribution

The authors construct two explicit biminimal pots realizing the cube and prove their uniqueness, countering the previous conjecture about their non-existence.

Findings

Two biminimal pots realizing the cube are explicitly constructed.

These two pots are shown to be unique up to isomorphism.

The conjecture about the non-existence of such pots is disproved.

Abstract

In this paper, we disprove a conjecture recently proposed in [L. Almodovar et al., arXiv:2108.00035] on the non-existence of biminimal pots realizing the cube, namely pots with the minimum number of tiles and the minimum number of bond-edge types. In particular, we present two biminimal pots realizing the cube and show that these two pots are unique up to isomorphisms.