This isn’t quite a near-miss to the Johnson solids, so I’m calling it a “near near-miss.” It could also be classified as a symmetrohedron. The pentagons and triangles are regular, but the red triangles have edges which are about 12% longer than those of the yellow triangles. The blue faces are isoceles trapezoids.

I found it while playing around with the great rhombicosidedcahedron using Stella 4d, which you can try for free right here.

I made this using Stella 4d, which you can try for free at this website.

Here’s another version of the same polyhedron, made using “rainbow color mode.”