# The Tetartoid

The Tetartoid

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.

{a,b,c}

a

b

c

{9,9,9}

{(4,8,20),(-4,-8,20),(-15,-15,15),(-20,-4,8),(-10,10,10)}

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.

(0,1/ϕ,1)

ϕ