Build geodesic domes by subdividing Platonic solids onto a sphere. Explore frequencies from 1v to 5v, toggle between icosahedron, octahedron and tetrahedron bases, and see the mathematics of spherical tessellation in 3D.
A geodesic dome subdivides a polyhedron face into smaller triangles projected onto a sphere. Higher frequencies (2v, 3v, 4v, 5v) produce more triangles and a rounder approximation. The formula F = f₀ × n² gives the face count.
Select a base polyhedron and subdivision frequency. Toggle wireframe/solid/both rendering. Switch between full sphere and dome (half-sphere) modes. The stats panel shows face, vertex and edge counts.
Buckminster Fuller patented the geodesic dome in 1954. The fullerene molecule (C60) — also called a 'buckyball' — has the same geometry as a frequency-1 truncated icosahedron.
This simulation builds geodesic spheres and domes by subdividing a Platonic solid and projecting each new vertex onto a unit sphere. Starting from an icosahedron, octahedron or tetrahedron, every triangular face is split into n² smaller triangles for a chosen frequency n (1v to 5v). The result approximates a sphere with near-uniform triangulation — the defining principle of Buckminster Fuller's geodesic geometry.
The Base selector chooses the starting polyhedron, while the Frequency slider sets the subdivision level n. Sphere and Dome buttons display the full surface or just the upper half, and Wireframe, Solid and Both control rendering. The live panel reports vertices, faces and edges, confirming Euler's formula V − E + F = 2. Such triangulated shells deliver remarkable strength-to-weight ratios, making them popular for greenhouses, planetariums and exhibition pavilions.
What is a geodesic dome?
A geodesic dome is a curved shell built from a network of triangles arranged on (or near) the surface of a sphere. It is generated by subdividing the faces of a polyhedron and pushing the new points outward onto a sphere, so the load is shared evenly across many short, triangulated struts.
What does the frequency control do?
Frequency n sets how finely each base face is divided: a face becomes n² smaller triangles. The slider ranges from 1v to 5v. Higher frequencies produce many more triangles and a smoother, rounder approximation of a true sphere, at the cost of more vertices and edges.
How is the face count calculated?
The total number of triangular faces is F = f₀ × n², where f₀ is the number of faces on the base solid — 20 for an icosahedron, 8 for an octahedron and 4 for a tetrahedron. The status bar shows this directly, for example 20 × 3² = 180 triangles for a 3v icosahedron.
The icosahedron has 20 equilateral faces and is the Platonic solid that most closely approximates a sphere, so its triangles need the least distortion when projected. This produces struts of more uniform length, which is why almost all real geodesic domes are based on the icosahedron rather than the octahedron or tetrahedron.
Dome mode keeps only the triangles whose centroid lies in the upper portion of the sphere (Y ≥ −0.05), discarding the lower faces. A ground disk and concentric rings are then drawn to represent the foundation, so you see a hemispherical shell sitting on a base rather than a complete floating sphere.
For any convex polyhedron, the vertices, edges and faces satisfy V − E + F = 2. The panel computes F = f₀n², E = 3F/2 (since each triangle has three edges shared between two faces) and V = F/2 + 2, then displays the sum so you can confirm it always equals 2.
No. When a flat face is subdivided and projected onto a sphere, the struts near the original vertices stretch slightly more than those near a face centre. Engineers classify these into a small number of distinct strut lengths, called chord factors, which is essential information for actually manufacturing a dome.
The fullerene molecule C₆₀, nicknamed a buckyball, has the shape of a truncated icosahedron — the same pattern as a football, with 12 pentagons and 20 hexagons. It was named after Buckminster Fuller because its closed, triangulated geodesic structure mirrors his domes.
Their high strength-to-weight ratio and efficient use of materials make them ideal for planetariums, greenhouses such as those at the Eden Project, radar radomes, exhibition pavilions and emergency shelters. The same geometry also appears in virtual sky domes and spherical sensor arrays.
The geometry is mathematically faithful: vertex positions, face counts and the projection onto a sphere are computed exactly. However, it is a visual and educational tool, not a structural analysis package — it does not model material stress, joint design, wind loads or the chord factors needed for a buildable dome.