The tetartoid has 12 identical irregular pentagonal faces. The mineral cobaltite sometimes occurs in this form. The individual pentagons can be generated from the arbitrary multiset , where , , and are non-negative. There are a few exceptions (like ), in which case "Error" is shown at the bottom of the control area, and a tetartoid based on the pentagon with vertices is shown instead.[more]
Names other than tetartoid include tetragonal pentagonal dodecahedron, pentagon-tritetrahedron, and tetrahedric pentagon dodecahedron. The combination gives a regular dodecahedron, where is the golden ratio.[less]
 Wikipedia. "Dodecahedron." (Aug 14, 2015) en.wikipedia.org/wiki/Dodecahedron.