Truncated dodecahedron

From Free net encyclopedia

Template:Semireg polyhedra db The truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.

Contents 1 Cartesian coordinates 2 Geometric relations 3 See also 4 External links

Image:Truncated dodecahedron flat.png

Cartesian coordinates

The following Cartesian coordinates define the vertices of a truncated dodecahedron centered at the origin:

(0, ±1/τ, ±(2+τ))

(±(2+τ), 0, ±1/τ)

(±1/τ, ±(2+τ), 0)

(±1/τ, ±τ, ±2τ)

(±2τ, ±1/τ, ±τ)

(±τ, ±2τ, ±1/τ)

(±τ, ±2, ±τ²)

(±τ², ±τ, ±2)

(±2, ±τ², ±τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Geometric relations

This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles.

See also

• Spinning truncated dodecahedron
• dodecahedron
• icosahedron
• icosidodecahedron
• truncated icosahedron

External links

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedraes:Dodecaedro truncado

nl:Afgeknotte dodecaëder pl:Dwunastościan ścięty pt:Dodecaedro truncado