Artists
Josep Rey Nadal
Mathematical artist and creative museographer
MMACA (Mathematics Museum of Catalonia)
La Garriga, Catalonia, Spain
Statement
Matemàtic, antic professor, artista, museògraf matemàtic i creatiu del MMACA (Museu de les Matemàtiques de Catalunya)
Artworks
Dos dotzes (Two twelve)
23.0 x 24.0 x 23.0 cm
Ironwood and beechwood
2024
Coupling of two dodecahedrons
Each one of the dodecahedrons has twelve faces, but one is made with regular pentagons and the other are rhombuses with diagonals in proportion √2.
Their symmetry system is different thus, they resist to couple.
The regular dodecahedron has 20 vertices and the rhombus 14 (8 with 3 faces and 6 with 4).
These 8 vertices are also coincident with some of the regular companion and they are also the vertices of a cube.
The regular dodecahedron is made with ironwood faces and the rhombus with beechwood edges.
Despite having different symmetry systems we can find a plane (actually 4) which, cutting the three polyhedra in a half (including the cube), the resulting section is a regular hexagon.