Square-pentagonal triswirlprism

{{Infobox polytope The square-pentagonal triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 12 pentagonal gyroprisms, 15 square gyroprisms, and 120 phyllic disphenoids. 2 pentagonal gyroprisms, 2 square gyroprisms, and 8 phyllic disphenoids join at each vertex It can be of two types obtained as a subsymmetrical faceting of the dodecagonal-pentadecagonal duoprism.
 * type=Isogonal
 * img=
 * off=auto
 * dim = 4
 * obsa =
 * cells = 60+60 phyllic disphenoids, 15 square gyroprisms, 12 pentagonal gyroprisms
 * faces = 120+120+120 scalene triangles, 15 squares, 12 pentagons
 * edges = 60+60+60+60+60
 * vertices = 60
 * verf = 10-vertex polyhedron with 4 tetragons and 8 triangles
 * symmetry = [{Square-pentagonal triswirlprismatic symmetry|(I{{sub|2}}(12)×I{{sub|2}}(15))+/3]], order 120
 * custom_measure = (based on square-pentagonal duoprisms of edge length 1)
 * el = Short side edges (60): $$\sqrt{\frac{35-10\sqrt3+\sqrt5-\sqrt{150+30\sqrt5}}{20}} ≈ 0.50901$$
 * el2 = Medial side edges (60): $$\sqrt{\frac{80-20\sqrt3+12\sqrt5-5\sqrt{30+6\sqrt5}-\sqrt{150+30\sqrt5}}{40}} ≈ 0.78282$$
 * el3 = Long side edges (60): $$\sqrt{\frac{25+\sqrt5-\sqrt{150+30\sqrt5}}{20}} ≈ 0.79064$$
 * el4 = Edges of squares (60): 1
 * el5 = Edges of pentagons (60): 1
 * circum = $$\sqrt{\frac{10+\sqrt5}{10}} ≈ 1.10617$$
 * dual = Square-pentagonal triswirltegum
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{20}{35-10\sqrt3+\sqrt5-\sqrt{150+30\sqrt5}}}$$ ≈ 1:1.96459.