31:T581,

Earth on a dodecahedron by C. Yamahata on Sketchfab
3D model created using the CAD software SpaceClaim (folded sheet tool). The starting point was the SVG file generated from this notebook.

32:T92a,// Slightly adapted from: https://observablehq.com/@fil/dodecahedral-projection function map(projection) { const context = DOM.context2d(width, width / 2); projection.fitExtent([[2,2],[width-2, width/2-2]], {type:"Sphere"}) var path = d3.geoPath(projection, context); context.beginPath(), path({type:"Sphere"}), context.fillStyle = sphere_fill, context.fill(); context.beginPath(), path(d3.geoGraticule()()), context.strokeStyle = graticule_stroke, context.stroke(); context.beginPath(), path(land), context.fillStyle = land_fill, context.fill(); context.beginPath(), path({type: "Sphere"}), context.strokeStyle = "#000", context.stroke(); if (show_equator){ context.beginPath(), path(d3.geoGraticule().step([0,100]).extent([[-179.99, -25], [179.99, 25]])()), context.strokeStyle = "red", context.stroke(); } // Polyhedral projections expose their structure as projection.root() // To draw them, we need to cancel the rotate var rotate = projection.rotate(); projection.rotate([0,0,0]); // Run the tree of faces to get all sites and folds var sites = [], folds = []; function recurse(face) { var site = d3.geoCentroid({type:"MultiPoint", coordinates:face.face}); site.id = face.id; sites.push(site); if (face.children) face.children.forEach(function(child){ folds.push({type:"LineString", coordinates: child.shared.map( e => d3.geoInterpolate(e, site)(1e-5) )}); recurse(child); }); } recurse((projection.tree || projection.root)()); // Sites & numbers if(show_structure){ context.beginPath(), path.pointRadius(10)({type:"MultiPoint", coordinates: sites}), context.fillStyle = "white", context.strokeStyle = "black", context.fill(), context.stroke(); sites.forEach(site => { context.textAlign = "center", context.fillStyle = "black", context.font = "16px Georgia", context.textBaseline = "middle", context.fillText(site.id, projection(site)[0], projection(site)[1] - 1); }); } // Folding lines folds.forEach(fold => { context.beginPath(), context.lineWidth = 0.5, context.setLineDash([3,4]), context.strokeStyle = "#888", path(fold), context.stroke(); }); // Restore the projection’s rotate projection.rotate(rotate); return context.canvas; }33:[{"id":"3c86f7c05418c62642aa705db5ba2384ad84b79b9462dac0e8f774d93125ac17c7fc76ef3ffdeee7413159c4269d922c9debf23f46622ead71aee6c848ada5d5","href":"https://static.observableusercontent.com/files/3c86f7c05418c62642aa705db5ba2384ad84b79b9462dac0e8f774d93125ac17c7fc76ef3ffdeee7413159c4269d922c9debf23f46622ead71aee6c848ada5d5","name":"110m_land.geojson","type":"application/geo+json","lastModified":1704214214609.911,"size":100851},{"id":"e103fda16f447ae0f35c77b261080a0db0bb7f0975395ed239ada2d6395a70869c75f31cd0fe503d8c85b97a0e525f7dd8e860fd8b64d73a3c89b0edd75296b2","href":"https://static.observableusercontent.com/files/e103fda16f447ae0f35c77b261080a0db0bb7f0975395ed239ada2d6395a70869c75f31cd0fe503d8c85b97a0e525f7dd8e860fd8b64d73a3c89b0edd75296b2","name":"world_dodecahedron.png","type":"image/png","lastModified":1704555718729.918,"size":653965},{"id":"5141e5d1df72ae9c5117bfab97b0bcf09458e303c47c9a3e2e3eaafca8bc4cded92361ee5cb0e2e78a214f4004f576b7bd3d24fb072a0442f04535a0e8af4c60","href":"https://static.observableusercontent.com/files/5141e5d1df72ae9c5117bfab97b0bcf09458e303c47c9a3e2e3eaafca8bc4cded92361ee5cb0e2e78a214f4004f576b7bd3d24fb072a0442f04535a0e8af4c60","name":"50m_land.geojson","type":"application/geo+json","lastModified":1705688314612.688,"size":1199365},{"id":"e0c2a2f9727d941563ce9f13f61c71fd3db74a98be78656258d4175762de4906ccbaf5a6ce1379ad9f15582efa6bfe686ca86f188736bb11d3e0dda81ac2ec65","href":"https://static.observableusercontent.com/files/e0c2a2f9727d941563ce9f13f61c71fd3db74a98be78656258d4175762de4906ccbaf5a6ce1379ad9f15582efa6bfe686ca86f188736bb11d3e0dda81ac2ec65","name":"10m_land.geojson","type":"application/geo+json","lastModified":1705694870194.173,"size":22384119}] 2f:{"title":"Dodecahedral projection","cells":[{"id":0,"value":"md`# Dodecahedral projection\n\n## Mapping the Earth: Optimal foldout on a dodecahedron.\n\nThis is a fork from [Philippe Rivière](https://observablehq.com/@fil)'s notebook on ***[Dodecahedral projection](https://observablehq.com/@fil/dodecahedral-projection)***.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1227,"value":"viewof land = Inputs.select(new Map([[\"High resolution map (very slow)\", land_10m], [\"Medium resolution map (slow)\", land_50m], [\"Low resolution map\", land_110m]]), {value: land_110m, label: \"Geo JSON map\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1045,"value":"// This SVG is kept intentionally hidden\nmap_svg = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":153,"value":"dodecahedron = { return map(projection); }","pinned":false,"hidden":false,"mode":"ojs"},{"id":1123,"value":"DOM.download(() => serialize(map_svg), \"dodecahedron\", \"Save as SVG\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":1134,"value":"
","pinned":false,"hidden":false,"mode":"html"},{"id":732,"value":"md`#### Parameters \n\nThe following parameters (three-axis rotation for geographic projections) can be set to slightly modify the position of the lands on the unfolded dodecahedron.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":570,"value":"viewof lambda = Inputs.range([240, 270], {value: 253, step: 0.5, label: \"lambda, λ (°)\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":573,"value":"viewof phi = Inputs.range([-40, -20], {value: -25, step: 0.5, label: \"phi, φ (°)\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":575,"value":"viewof gamma = Inputs.range([-30, -20], {value: -26, step: 0.5, label: \"gamma, γ (°)\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":811,"value":"
","pinned":false,"hidden":false,"mode":"html"},{"id":726,"value":"md`##### Optional features\n\nAs for the arrangement of the faces (see tile #), the default layout used is that proposed by Jarke J. van Wijk in Fig. 8 of “[Unfolding the Earth: Myriahedral Projections](https://doi.org/10.1179/000870408X276594),” *The Cartographic Journal*, Vol. 45 No. 1 pp. 32–42, February 2008.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":859,"value":"viewof parents = Inputs.select(new Map([[\"Jarke J. van Wijk\", parents_Jarke_J_van_Wijk], [\"Other (1): Unsplit US territory\", parents_1], [\"Other (2): Americas + Antarctica\", parents_2], [\"Other (3): Unsplit Florida\", parents_3], [\"Other (4): Centered on Antarctica\", parents_4], [\"Other (5): From Japan to New Zeland\", parents_5], [\"Other (6):Centered on Arctica\", parents_6], [\"Other (7): Two flowers\", parents_7]]), {value: parents_Jarke_J_van_Wijk, label: \"Arrangement\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":657,"value":"viewof show_structure = Inputs.toggle({ label: \"Structure (tile #)\", value: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":694,"value":"viewof show_equator = Inputs.toggle({ label: \"Equator\", value: true })","pinned":false,"hidden":false,"mode":"ojs"},{"id":1273,"value":"
","pinned":false,"hidden":false,"mode":"html"},{"id":1267,"value":"#### 3D model\nHere are two models created from the SVG file generated above.","pinned":false,"hidden":false,"mode":"md"},{"id":1257,"value":"$31","pinned":false,"hidden":false,"mode":"html"},{"id":1138,"value":"\n

**The Earth on a dodecahedron.** Map printed on an A4 sheet from the SVG file generated from this notebook.

","pinned":false,"hidden":false,"mode":"html"},{"id":416,"value":"md`-----\n### Appendix`","pinned":false,"hidden":false,"mode":"ojs"},{"id":832,"value":"parents_Jarke_J_van_Wijk = [-1, 2, 0, 1, 1, 0, 4, 5, 3, 10, 7, 8]","pinned":false,"hidden":false,"mode":"ojs"},{"id":887,"value":"parents_1 = [-1, 2, 0, 1, 1, 0, 4, 0, 3, 10, 7, 8]","pinned":false,"hidden":false,"mode":"ojs"},{"id":870,"value":"parents_2 = [-1, 3, 1, 8, 1, 0, 4, 5, 11, 10, 7, 7]","pinned":false,"hidden":false,"mode":"ojs"},{"id":906,"value":"parents_3 = [-1, 3, 1, 8, 1, 0, 4, 0, 11, 10, 7, 7]","pinned":false,"hidden":false,"mode":"ojs"},{"id":829,"value":"parents_4 = [-1, 3, 1, 8, 1, 0, 4, 5, 11, 10, 7, 9]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1186,"value":"parents_5 = [-1, 3, 0, 8, 1, 0, 4, 0, 11, 10, 7, 9]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1178,"value":"parents_6 = [-1, 0, 1, 1, 1, 0, 4, 0, 3, 10, 7, 3]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1210,"value":"parents_7 = [-1, 0, 0, 0, 9, 0, 9, 0, 3, 8, 9, 9]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1085,"value":"land_fill = \"#022\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1090,"value":"sphere_fill = \"#dfeef0\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1101,"value":"graticule_stroke = \"#ccc\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":603,"value":"land_110m = {return await FileAttachment(\"110m_land.geojson\").json();}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1230,"value":"land_50m = {return await FileAttachment(\"50m_land.geojson\").json();}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1243,"value":"land_10m = {return await FileAttachment(\"10m_land.geojson\").json();}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1050,"value":"projection = d3.geoDodecahedral()\n .parents(parents)\n .angle(0)\n .rotate([lambda, phi, gamma])","pinned":false,"hidden":false,"mode":"ojs"},{"id":1053,"value":"path = d3.geoPath(projection)","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":1125,"value":"serialize = {\n const xmlns = \"http://www.w3.org/2000/xmlns/\";\n const xlinkns = \"http://www.w3.org/1999/xlink\";\n const svgns = \"http://www.w3.org/2000/svg\";\n return function serialize(svg) {\n svg = svg.cloneNode(true);\n const fragment = window.location.href + \"#\";\n const walker = document.createTreeWalker(svg, NodeFilter.SHOW_ELEMENT);\n while (walker.nextNode()) {\n for (const attr of walker.currentNode.attributes) {\n if (attr.value.includes(fragment)) {\n attr.value = attr.value.replace(fragment, \"#\");\n }\n }\n }\n svg.setAttributeNS(xmlns, \"xmlns\", svgns);\n svg.setAttributeNS(xmlns, \"xmlns:xlink\", xlinkns);\n const serializer = new window.XMLSerializer;\n const string = serializer.serializeToString(svg);\n return new Blob([string], {type: \"image/svg+xml\"});\n };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"d3 = require(\"d3-geo\", \"d3-fetch\", \"d3-geo-polygon\")","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}