The snub cube can be made with 4 colors and has only square and equilateral triangle faces. Like a cube, it has 6 square faces that are made in 3 colors. Opposite squares in the polyhedron are in parallel planes and are the same color but unlike a cube, their faces are slightly twisted. Each square face is surrounded by triangles made of the same color ... one of the 3 colors of the square faces. For instance, in my polyhedron each red square face is surrounded by 4 brown triangles. Each brown square face is surrounded by 4 yellow triangles and each yellow square face is surrounded by 4 red triangles.
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The fourth color of this polyhedron is used to fill in the missing gaps in the polyhedron.
Begin your construction by making two squares each surrounded by 4 triangles. These square will be adjacent sides in your cube. In my example I began with a red square surrounded by brown triangles. I attached my brown square surrounded by yellow triangles with one yellow triangle adding to the gap between brown triangles. My orange triangles completed the gap. Around the red square face will be two brown square faces and two yellow square faces, each surrounded by triangles with the orange triangles always filling the gaps.