The Golden Rational Tetrahedra in Zome

The Zome system is a construction toy based on the golden ratio and the icosahedral group. There are four main colors of struts based on vectors: blue , red , yellow and green . Struts scale up in length by powers of .
Recently, all the tetrahedra with rational dihedral angles on all edges were determined [1]. All 19 of these can be represented in the Zome system. For these, the dihedral angles are shown on the edges and the solid angles are shown at the vertices, both as fractions of . In addition, other tetrahedra can be made. The angles are no longer simple, so they are not shown.


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[1] K. S. Kedlaya, A. Kolpakov, B. Poonen and M. Rubinstein, "Space Vectors Forming Rational Angles."
[2] S. Vorthmann. "Zometool Tetrahedra Challenge Solution." (Nov 16, 2023)
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