Sawing an Eighth from a Bilinski Dodecahedron

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This Demonstration shows how to saw an eighth of a Bilinski dodecahedron from a rectangular stick of width 1 and height golden ratio.

Contributed by: Izidor Hafner and Franc Savnik (April 2019)
Open content licensed under CC BY-NC-SA



Savnik used Donald Bell's method to make a wooden model of a Bilinski dodecahedron. In 1959, Savnik was Bilinski's student at the University of Zagreb (Croatia) [4]. From a mathematical viewpoint, the main problem is calculating the angle between the working table and the basic face of the wooden stick so that the cut produces a golden rhombus.


[1] S. Bilinski, "Über die Rhombenisoeder," Glasnik, 15, 1960 pp. 251–263.

[2] I. Hafner and T. Zitko. "A Dissection of Two Rhombic Dodecahedra of the Second Kind to a Cube." (Apr 26, 2019)

[3] I. Hafner and T. Zitko. "A Dissection of Quarter of Rhombic Dodecahedron of the Second Kind to a Cube." (Apr 26, 2019)

[4] F. Savnik. "Arts and Crafts Products." (Apr 26, 2019) 3_en.html.

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