On Alan Schoen's I-WP Minimal Surface

TL;DR

This paper explores Alan Schoen's I-WP minimal surface, providing geometric realizations and analyzing its associate family, revealing symmetries and congruences at specific Bonnet angles.

Contribution

It offers detailed geometric realizations of the I-WP surface and proves its associate family contains six congruent surfaces at specific Bonnet angles.

Findings

Six congruent I-WP surfaces at Bonnet angles multiples of 60°

Multiple geometric realizations with the same conformal structure

Confirmation of cubical symmetries in the I-WP surface

Abstract

We discuss in detail Alan Schoen's I-WP surface, an embedded triply periodic minimal surface of genus 4 with cubical symmetries. We exhibit various geometric realizations of this surface with the same conformal structure and use them to prove that the associate family of the I-WP surface contains six surfaces congruent to I-WP at Bonnet angles that are multiples of $60^\circ$.