{"schemaVersion":1,"record":{"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}],"sections":[{"id":"principle","title":"How it works","body":"Convert a form and display its properties."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-geometry-variants\"></a>\n\n- 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. <a id=\"variant-dissection\"></a>\n- Division of area. Definition: Make cuts to obtain parts of equal or specified area. Conditional example: Divide a polygon into three equal parts. <a id=\"variant-equal-area-cut\"></a>\n- 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. <a id=\"variant-limited-lines\"></a>\n- 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. <a id=\"variant-origami\"></a>\n- Drawing after bending. Definition: Restore the appearance of a folded or unfolded sheet using holes and cuts. Conditional example: Predict the pattern after unfolding. <a id=\"variant-folded-pattern\"></a>\n- 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. <a id=\"variant-flexagon\"></a>\n- 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. <a id=\"variant-net-solid\"></a>\n- 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. <a id=\"variant-geometric-construction\"></a>\n- Completing symmetry. Definition: Add or move elements to obtain a given symmetry. Conditional example: Complete a pattern relative to two axes. <a id=\"variant-reflection-symmetry\"></a>\n- 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. <a id=\"variant-perimeter-area\"></a>"},{"id":"context","title":"Context and limits","body":"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."}],"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"}}