--- key: mechanic/puzzle--family-geometry type: mechanic id: puzzle--family-geometry lang: en title: 'Geometry, cutting and folding' summary: >- The player folds, cuts or transforms a shape and uses the resulting geometry to solve the puzzle. updatedAt: '2026-10-22' status: active url: 'https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-geometry/' jsonUrl: >- https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-geometry.json markdownUrl: >- https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-geometry.md aliases: [] tags: - Puzzles - Mechanics catalog sourceIds: - source-a4c131ce094457fb sources: - id: source-a4c131ce094457fb title: Paper Trail url: 'https://store.steampowered.com/app/1889740/' verifiedAt: null relations: [] placements: - catalogId: puzzle id: family-geometry title: Puzzles url: 'https://gamemechanics.pro/en/mechanics/puzzle/#family-geometry' categoryIds: - section-1 supersededBy: [] attributes: preview: updatedAt: '2026-10-22' title: 'Geometry, cutting and folding' description: >- The player folds, cuts or transforms a shape and uses the resulting geometry to solve the puzzle. image: src: images/mechanics/adventure-paper-trail-00.webp width: 1440 height: 810 game: Paper Trail sourceUrl: 'https://store.steampowered.com/app/1889740/' originalUrl: >- https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/1889740/ss_1469a801a268e771e65b1c58f2930a9b33614e5d.1920x1080.jpg?t=1750783735 credit: Newfangled Games rights: >- Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0. caption: A paper fold changes the shape of the play space alt: A paper fold changes the shape of the play space markers: - x: 74 'y': 60 label: The fold boundary changes the available shape tips: - >- Keep the relationship between the original shape and the transformation clear. examples: - title: Paper Trail url: 'https://store.steampowered.com/app/1889740/' endsAt: null provenance: >- Original editorial design catalog consolidated from project discussions on 2026-10-20. Complete discussion item lists and contextual limitations are preserved; linked primary sources support specific techniques, not the entire classification. English translation was prepared with machine assistance and editorial review. license: CC-BY-4.0 codeLicense: MIT attribution: gamemechanics.pro contributors catalogKey: catalog/puzzle --- # Geometry, cutting and folding id: puzzle--family-geometry type: mechanic key: mechanic/puzzle--family-geometry lang: en status: active url: https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-geometry/ The player folds, cuts or transforms a shape and uses the resulting geometry to solve the puzzle. ## At a glance ![A paper fold changes the shape of the play space](https://gamemechanics.pro/images/mechanics/adventure-paper-trail-00.webp) [Paper Trail](https://store.steampowered.com/app/1889740/) · Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0. 1. The fold boundary changes the available shape - Keep the relationship between the original shape and the transformation clear. - [Paper Trail](https://store.steampowered.com/app/1889740/) ## How it works Convert a form and display its properties. ## Variants ### Variants and applications - Cutting and rearranging. Definition: Divide a figure into parts from which the required shape is assembled. Conditional example: Turn a rectangle into a square with several cuts. - Division of area. Definition: Make cuts to obtain parts of equal or specified area. Conditional example: Divide a polygon into three equal parts. - Construction with a limited number of lines. Definition: Cover or connect points with a limit of straight lines and breaks. Conditional example: Connect nine points with four segments. - Folding the sheet. Definition: Select a sequence of folds to obtain a shape or align marks. Conditional example: Align holes with several folds. Terms: origami; origami. - Drawing after bending. Definition: Restore the appearance of a folded or unfolded sheet using holes and cuts. Conditional example: Predict the pattern after unfolding. - Rearranging hinged surfaces. Definition: To obtain the desired edge or pattern through the allowable bends of a composite structure. Conditional example: To reveal the hidden side of a flexagon. Terms: flexagon; flexagon. - Development and volume. Definition: Compare a flat development with a spatial body. Conditional example: Select a development of a cube with the desired adjacent faces. - Constructing a figure with tools. Definition: Obtain an exact object using allowed geometric operations. Conditional example: Construct the center of a circle using allowed actions. - Completing symmetry. Definition: Add or move elements to obtain a given symmetry. Conditional example: Complete a pattern relative to two axes. - Separation of area and perimeter. Definition: Change shape by maintaining one geometric property and changing another. Conditional example: Increase the perimeter while maintaining the area. ## Context and limits A wide catalog of mechanics for digital puzzles, paper logic problems and physical puzzles. Each position contains an action or rule and a conditional example of application. ## Connected materials ## Sources and provenance Original editorial design catalog consolidated from project discussions on 2026-10-20. Complete discussion item lists and contextual limitations are preserved; linked primary sources support specific techniques, not the entire classification. English translation was prepared with machine assistance and editorial review. - [Paper Trail](https://store.steampowered.com/app/1889740/) (id: source-a4c131ce094457fb) CC-BY-4.0 · gamemechanics.pro contributors