2. Kowalewski's Coloring of the Triacontahedron

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Kowalewski colored the rhombic triacontahedron with five or six colors.


Coloring with five colors consists of dividing the 30 faces of the solid into five groups. A group consists of six faces such that two faces in it are either parallel or perpendicular to each other.

The solid can be covered by six bands, each consisting of 10 faces. Each face of the solid is common to two bands. Bands are colored by different colors and arranged with crossings going alternately over and under. A face is colored by the color of the band that is going over it.

The solid is represented with a map projection into 2D or as a 3D solid; you can choose the colors for the faces.


Contributed by: Izidor Hafner (August 2019)
Open content licensed under CC BY-NC-SA



[1] G. Kowalewski and D. Booth, "Construction Games with Kepler's Solid," Austin, TX: Parker Courtney Press, 2001. (Jul 16, 2019) www.zometool.com/content/KowalewskiWeb.pdf.


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