The Tetartoid

a

b

c

1

2

3

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

{a,b,c}

, where

a

,

b

, and

c

are non-negative. There are a few exceptions (like

{9,9,9}

), in which case "Error" is shown at the bottom of the control area, and a tetartoid based on the pentagon with vertices

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

is shown instead.

Names other than tetartoid include tetragonal pentagonal dodecahedron, pentagon-tritetrahedron, and tetrahedric pentagon dodecahedron. The combination

(0,1/ϕ,1)

gives a regular dodecahedron, where

ϕ

is the golden ratio.