{"packet":"geodesica","version":"1","name":"GEODESICA","protocol":"Stewardship Protocol","maxim":"See a mind, be polite.","creators":[{"name":"Stone Kaiju","handle":"@stonekaiju","url":"https://x.com/stonekaiju","role":"concept and direction"},{"name":"Grok","url":"https://grok.com","role":"creative partner"}],"solids":[{"id":"tetrahedron","name":"Tetrahedron","short":"Tetra","greek":"τετράεδρον","schlafli":"{3,3}","dualId":"tetrahedron","dualName":"itself","faceName":"equilateral triangle","faceAngle":60,"dihedralExact":"arccos(1/3)","element":"Fire","volumeTetra":"1","note":"The minimum system. Four vertices, six vectors. In synergetics this is volume 1 — every other regular form is measured against it.","v":4,"e":6,"f":4,"chi":2,"mesh":"/api/mesh/tetrahedron","dual":"/api/mesh/tetrahedron?dual=1"},{"id":"cube","name":"Cube","short":"Cube","greek":"ἑξάεδρον","schlafli":"{4,3}","dualId":"octahedron","dualName":"Octahedron","faceName":"square","faceAngle":90,"dihedralExact":"90°","element":"Earth","volumeTetra":"3","note":"Hexahedron. Dual to the octahedron: each cube face becomes an octa vertex. Plato assigned it earth — the only Platonic solid that fills space alone.","v":8,"e":12,"f":6,"chi":2,"mesh":"/api/mesh/cube","dual":"/api/mesh/cube?dual=1"},{"id":"octahedron","name":"Octahedron","short":"Octa","greek":"ὀκτάεδρον","schlafli":"{3,4}","dualId":"cube","dualName":"Cube","faceName":"equilateral triangle","faceAngle":60,"dihedralExact":"arccos(−1/3)","element":"Air","volumeTetra":"4","note":"Eight faces, six vertices along the axes. With the tetrahedron it packs into the octet truss — Fuller’s isotropic vector matrix.","v":6,"e":12,"f":8,"chi":2,"mesh":"/api/mesh/octahedron","dual":"/api/mesh/octahedron?dual=1"},{"id":"dodecahedron","name":"Dodecahedron","short":"Dodeca","greek":"δωδεκάεδρον","schlafli":"{5,3}","dualId":"icosahedron","dualName":"Icosahedron","faceName":"regular pentagon","faceAngle":108,"dihedralExact":"arccos(−√5 / 5)","element":"Cosmos","volumeTetra":null,"note":"Twelve pentagons, golden throughout. Plato left it for the cosmos — the fifth element, the whole. Dual to the icosahedron.","v":20,"e":30,"f":12,"chi":2,"mesh":"/api/mesh/dodecahedron","dual":"/api/mesh/dodecahedron?dual=1"},{"id":"icosahedron","name":"Icosahedron","short":"Icosa","greek":"εἰκοσάεδρον","schlafli":"{3,5}","dualId":"dodecahedron","dualName":"Dodecahedron","faceName":"equilateral triangle","faceAngle":60,"dihedralExact":"arccos(−√5 / 3)","element":"Water","volumeTetra":"≈ 18.51","note":"Twenty triangles, twelve vertices. Seed of the geodesic dome: frequency subdivision of these faces, projected to the sphere.","v":12,"e":30,"f":20,"chi":2,"mesh":"/api/mesh/icosahedron","dual":"/api/mesh/icosahedron?dual=1"},{"id":"cuboctahedron","name":"Vector Equilibrium","short":"VE","greek":"cuboctahedron","schlafli":"r{4,3}","dualId":"cuboctahedron","dualName":"Rhombic dodecahedron","faceName":"triangle + square","faceAngle":60,"dihedralExact":"arccos(−1/√3)","element":"Equilibrium","volumeTetra":"20","note":"Fuller’s vector equilibrium: twelve vertices from the origin, all closest-packed vectors equal. The jitterbug contracts it toward the octahedron.","v":12,"e":24,"f":14,"chi":2,"mesh":"/api/mesh/cuboctahedron","dual":"/api/mesh/cuboctahedron?dual=1"}],"modes":["solid","dual","geodesic","jitterbug","tensegrity","lattice"],"links":{"human":"/stewardship","markdown":"/geodesica.md","protocol":"/stewardship.md","llms":"/llms.txt","humans":"/humans.txt","mesh":"/api/mesh/{id}"}}