Origami & Geometry

Folding Sequences and Paper Geometry

A structured look at how flat sheets acquire three-dimensional form through crease patterns, fold sequences, and geometric constraint.

Origami paper cranes folded from coloured square sheets

Folding topics

Three areas of paper geometry covered in depth: the logic of crease diagrams, the mechanics of pleating, and the combinatorics of modular assembly.

Huzita–Hatori axiom 7 diagram illustrating geometric fold rules
Geometry

Crease Patterns and Paper Geometry

How fold lines encode geometric structure, from the Huzita–Hatori axioms to the constraints that govern flat-foldability.

June 2025 · Geometry
Diagram of the waterbomb base fold with valley and mountain creases marked
Folding

Waterbomb Base and Pleating Sequences

The waterbomb base as an entry point into radial symmetry, followed by accordion and sink folds used in tessellation work.

June 2025 · Folding
Assembled modular origami polyhedron made from identical folded units
Modular

Modular Origami and Polyhedral Forms

Sonobe units, PHiZZ connectors, and the combinatorial logic behind assembling identical modules into stable polyhedral shells.

June 2025 · Modular

Tessellations and geometric forms

Selected images from Wikimedia Commons illustrating origami tessellations, structural units, and folded geometry.

Miura-ori fold tessellation — a rigid-foldable pattern used in deployable structures
Miura-ori tessellation — Wikimedia Commons
Origami rose tessellation showing periodic repetition of a twist-fold unit
Rose tessellation — Wikimedia Commons
Non-periodic origami tessellation where no translational unit cell repeats
Non-periodic tessellation — Wikimedia Commons

Folding geometry in Polish context

Triquane documents fold sequences, crease diagrams, and structural origami forms as studied and practiced in Poland.

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