GART

Geodesic Polyhedron

A Platonic solid, geodesically subdivided, drawn as 2D line art. Detail is subdivision; turn and tilt choose the view. Far side fades the hidden hemisphere so the solid reads in depth.

Geodesic Polyhedron: A Platonic solid, geodesically subdivided, drawn as 2D line art. Detail is subdivision; turn and tilt choose the view. Far side fades the hidden hemisphere so the solid reads in depth.Geodesic Polyhedron: A Platonic solid, geodesically subdivided, drawn as 2D line art. Detail is subdivision; turn and tilt choose the view. Far side fades the hidden hemisphere so the solid reads in depth.

About this shape

R. Buckminster Fuller's domes · Michael Goldberg, 1937

Geodesic Polyhedron, goldberg polyhedron, drawn by GART: A Platonic solid, geodesically subdivided, drawn as 2D line art. Detail is subdivision; turn and tilt choose the view. Far side fades the hidden hemisphere so the solid reads in depth.
Geodesic Polyhedron · CC BY 4.0

Start from a Platonic solid, subdivide each face toward a sphere, and project the vertices back out. What you see is a 2D line drawing of that mesh: tilt is the view, Far side fades the hidden hemisphere so the solid reads in depth.

TopicsPolyhedron (opens in a new tab)Geodesic polyhedron (opens in a new tab)Goldberg polyhedron (opens in a new tab)

1D fold
A triangle belt. Twenty faces, one hinge line.

Behind the mathematics

R. Buckminster Fuller1895–1983

The geodesic dome

American architect and designer who patented the geodesic dome, a sphere approximated by a light lattice of triangles.

Michael Goldberg1902–1990

Goldberg polyhedra, 1937

American mathematician who in 1937 described the family of nearly spherical polyhedra built from hexagons and twelve pentagons.