This 122-faced solid is the dual of the convex hull of the compound of the rhombicosidodecahedron and its dual, the strombic hexecontahedron. Its regular faces are 20 triangles, 12 pentagons, and 30 squares. It also has 60 faces which are isosceles trapezoids.

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If we take the side of the pentagon equal to 1, how long is the side of the square? – and how long is the side of the triangle?

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1.8376 and 2.9733 are the base lengths of the trapezoids, and the leg length is 2.5987. That should give you the answers you seek pretty easily.

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Thanks…

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