In this symmetrohedron, all faces are regular, except for the green isosceles triangles. If these triangles were a little closer to being regular, this would be a near-miss to the Johnson solids, but that is not the case. I made this (starting with the last polyhedron in the post right before this one) using Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.
RobertLovesPi.net 
What are the proportions of the green isosceles triangles?
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Those triangles have vertex angles of 53.7 degrees, and have bases that are about 10% shorter than their legs.
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thanks
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You’re welcome!
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Very nice indeed.
Suppose, the green triangles were constructed based on some property of polyhedron itself, like all vertices are on the same sphere and/or large edges of green triangles together with edges of blue triangles form planar regular (?) 20-gon.
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I really like the construction.
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Thank you!
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