{"openapi":"3.1.0","info":{"title":"Geometric Solids API","version":"1.0.0","description":"Advanced 3D-solid geometry as an API, computed locally and deterministically — the shapes a basic geometry calculator leaves out. The cone-frustum endpoint gives the volume V = (π·h/3)·(R² + R·r + r²), the slant height √(h² + (R−r)²) and the lateral and total surface area of a truncated cone, the shape of buckets, lampshades and hoppers. The torus endpoint gives a doughnut’s volume 2π²·R·r² and surface area 4π²·R·r from its centre-to-tube and tube radii. The ellipsoid endpoint gives the exact volume (4/3)π·a·b·c and a Knud-Thomsen surface-area approximation accurate to better than 1.1 %. The platonic endpoint returns the volume and surface area of any of the five Platonic solids — tetrahedron, cube, octahedron, dodecahedron and icosahedron — from the edge length, using the exact golden-ratio coefficients (a unit icosahedron has volume 2.1817 and surface area 8.6603). Use a consistent length unit and get area and volume out. Everything is computed locally and deterministically, so it is instant and private. Ideal for engineering, CAD, 3D-modelling, architecture, manufacturing and maths-education app developers, volume-and-area and packaging tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. These are the advanced solids; for sphere, cube, cylinder, cone and 2D shapes use a general geometry API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/solids-api","description":"oanor gateway"}],"tags":[{"name":"Solids"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/cone-frustum":{"get":{"operationId":"get_v1_cone_frustum","tags":["Solids"],"summary":"Truncated cone","description":"","parameters":[{"name":"radius_bottom","in":"query","required":true,"description":"Bottom radius R","schema":{"type":"string"},"example":"5"},{"name":"radius_top","in":"query","required":true,"description":"Top radius r","schema":{"type":"string"},"example":"3"},{"name":"height","in":"query","required":true,"description":"Height h","schema":{"type":"string"},"example":"4"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Cone frustum (truncated cone): V = (π·h/3)·(R² + R·r + r²); lateral area = π(R+r)·√(h² + (R−r)²).","inputs":{"height":4,"radius_top":3,"radius_bottom":5},"volume":205.25072,"slant_height":4.472136,"total_surface_area":219.211186,"lateral_surface_area":112.397036},"meta":{"timestamp":"2026-06-05T19:50:11.222Z","request_id":"1dbda7c9-7956-499f-bce8-86d7c059d4eb"},"status":"ok","message":"Cone frustum","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/ellipsoid":{"get":{"operationId":"get_v1_ellipsoid","tags":["Solids"],"summary":"Ellipsoid","description":"","parameters":[{"name":"a","in":"query","required":true,"description":"Semi-axis a","schema":{"type":"string"},"example":"3"},{"name":"b","in":"query","required":true,"description":"Semi-axis b","schema":{"type":"string"},"example":"4"},{"name":"c","in":"query","required":true,"description":"Semi-axis c","schema":{"type":"string"},"example":"5"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Ellipsoid: V = (4/3)π·a·b·c (exact); surface area by the Knud Thomsen approximation (error < 1.1%). With a=b=c it reduces to a sphere.","inputs":{"a":3,"b":4,"c":5},"volume":251.327412,"surface_area_approx":199.501704},"meta":{"timestamp":"2026-06-05T19:50:11.332Z","request_id":"9a0454b4-5073-4e48-b80e-6b1390069e8a"},"status":"ok","message":"Ellipsoid","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/platonic":{"get":{"operationId":"get_v1_platonic","tags":["Solids"],"summary":"Platonic solid","description":"","parameters":[{"name":"solid","in":"query","required":true,"description":"tetrahedron, cube, octahedron, dodecahedron, icosahedron","schema":{"type":"string"},"example":"icosahedron"},{"name":"edge","in":"query","required":true,"description":"Edge length","schema":{"type":"string"},"example":"1"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Platonic solid from edge length a. Cube: V=a³, S=6a². Tetrahedron: V=a³/(6√2). 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