# polyhedra and classical art

Leonardo da Vinci's polyhedra

This truncated icosahedron represented with "solid edges" is one of the illustrations of The Divine Proportion  (Lucas Pacioli)

Luca Pacioli's polyhedron

The polyhedron on the top left of this portrait of Luca Pacioli is a glass small rhombicuboctahedron half-filled with water.

marble and wooden polyhedra

marble mosaic, Saint Mark's basilica in Venice
(small stellated dodecahedron)

polyhedra engraved on wood in the church of Santa Maria of Organo in Verona

Dürer's polyhedron
With its 8 faces (2 equilateral triangles and 6 symmetric pentagons), this polyhedron is a truncated rhombohedron: first stretch a cube along one diagonal, then cut the two peaks so that the remaining solid is inscribed in a sphere.

 a pentagonal face Its dual is a dodecahedron with triangular isosceles faces (triangular antiprism biaugmented by two tetrahedra).
engraving Melencholia I

Remark: At the top right of the engraving there is also a magic square of order 4 (4x4 boxes containing the integers from 1 to 16) with beautiful properties.

 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1
Many sums of four boxes are equal to 34=(1+2+3+...+15+16)/4
• the four lines, the four columns and the two diagonals
• the four 2x2 squares of the corners and the one of the center
• the vertices of three "big" squares: 16+13+1+4   3+8+14+9   2+12+15+5
• the vertices of four rectangles: 3+2+14+15   5+9+12+8   3+5+14+12   2+8+15+9
The sums of two boxes symmetrical with respect to the center have all the same value 17=34/2
And on the bottom line there is also the date of completion of the engraving (1514).
a curious stone polyhedron

There are two ways to build this polyhedron:
•  excavate twelve triangular prisms on a cube truncated at the third by the vertices (in red),
•  augment a cube truncated by the edges and the vertices (in green) with eight flat triangular antiprisms.

sculpture in a cemetery, Pays Basque (France)
(photo by André Brzezinski)

polyhedra in M. C. Escher's work

Reptiles

Gravity

Stars

 compound of two tetrahedra compound of two cubes small stellated dodecahedron
 stellated cuboctahedron compound of three octahedra
 compound of three cubes stellated rhombidodecahedron

Waterfall

 Salvator Daly A shape of a regular dodecahedron appears in the decor of Sacrament of the Last Supper. Corpus Hypercubus (the "cross" is a net of the hypercube)
 along the streets along a 3-fold axisthe stellateddodecahedronlooks like a star of David Escher Museum - (The Hague - Netherlands) stellate dodecahedra on fence (Great Synagogue - Paris)

more polyhedral art: modern - architecture

 home page convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects November 2004updated 28-05-2019