Triangular-pentagonal duoantiprismatic antiprism

The triangular-pentagonal duoantiprismatic antiprism, or trapedapap, is a convex isogonal polyteron that consists of 2 triangular-pentagonal duoantiprisms, 6 digonal-pentagonal duoantiprisms, 10 digonal-triangular duoantiprisms, and 60 digonal disphenoidal pyramids. 1 triangular-pentagonal duoantiprism, 2 digonal-pentagonal duoantiprisms, 2 digonal-triangular duoantiprisms, and 5 digonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the hexagonal-decagonal duoprismatic prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{75+9\sqrt5}{58}}$$ ≈ 1:1.28066.