Exploring criteria for designing novel waterbomb tessellations using triangular convex polygons

TL;DR

This paper investigates criteria for designing novel waterbomb tessellations using triangular convex polygons, expanding the understanding and potential applications of these patterns in origami design.

Contribution

It introduces new criteria for generalizing waterbomb tessellations and uncovers novel patterns, focusing on triangular polygons, with discussions on foldability and future generalizations.

Findings

Uncovered new waterbomb tessellations with potential design applications

Established criteria for generalizing waterbomb tessellations

Discussed foldability properties and future polygon generalizations

Abstract

Waterbomb style tessellations have been explored in the past by artists such as Ronald D. Resch, Benjamin Parker and Mitya Miller. Generalised waterbomb tessellations are still underexplored in origami design. We have explored various sets of criteria for generalising waterbomb tessellations in order to enumerate valid patterns. We only consider triangular waterbomb tessellations, other polygons will be explored in future papers. In our search we have uncovered some new waterbomb tessellations, which could offer new uses in representational and geometric origami design. We conclude by discussing foldability properties and possible generalisations.