Steinhaus Dodecahedron

A dodec­a­he­dron (from Greek δώδεκα — twelve and εδρον — face) — is one of five reg­u­lar reg­u­lar poly­he­dra. It has 12 faces, which are reg­u­lar pen­tagons, 30 edges, 20 ver­tices.

The idea of a model is pro­posed in Hugo Stein­haus' book ”Math­e­mat­i­cal snap­shots” (first edi­tion in Russ­ian: Moscow-Leningrad, 1949).

A model can be man­u­fac­tured of thick card­board. Cor­ru­gated card­board, for exam­ple, that boxes for office paper are made of, would suf­fice. A rub­ber band — like the one a roll of money is binded with — is also needed. In this case the dodec­a­he­dron's edge should be around 5 cen­time­ters long.

The lay­out of the dodec­a­he­dron half can be printed on a sheet of reg­u­lar paper to mark the shape for cut­ting from card­board.