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Platonic Solids · 3D

Icosahedron

{3,5} · Water

Icosahedron, drawn as a glowing line figure

Twenty triangles, nearly round and rolling like a droplet: water. Its twelve corners are three golden rectangles at right angles.

Vertices
12
Edges
30
Faces
20
Dihedral
138.19°

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Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane or lift it into four dimensions.

Facts

  • Its vertices are the corners of three mutually perpendicular golden rectangles.
  • Seen along a vertex axis its shadow shows a decagon of fives.
  • Many viruses build their shells as icosahedra.
  • It is the most sphere-like Platonic solid by volume in its circumsphere.

History and meaning

Plato gave it to water, which flows. The golden ratio φ threads through every coordinate: (0, ±1, ±φ).

Across the dimensions

  • Around a corner of 600-CellIn the 600-cell, the twelve neighbours of every vertex form an icosahedron.
  • Dual Dodecahedron

Learn it step by step

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