Heptagonal duoexpandoprism

{{Infobox polytope }obsa = Hedep The heptagonal duoexpandoprism or hedep is a convex isogonal polychoron and the fifth member of the duoexpandoprism family. It consists of 28 heptagonal prisms of two kinds, 49 rectangular traapezoprisms, 98 wedges, and 49 tetragonal disphenoids. 2 heptagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal heptagonal-tetradecagonal duoprisms, or more generally heptagonal-diheptagonal duoprisms, and a subset of its variations can be constructed by expanding the cells of the heptagonal duoprism outward.. However, it cannot be made uniform.
 * type=Isogonal
 * dim = 4
 * img=
 * off=auto
 * cells = 49 tetragonal disphenoids, 98 wedges, 49 rectangular trapezoprisms, 14+14 heptagonal prisms
 * faces = 196 isosceles triangles, 98+98 rectangles, 196 isosceles trapezoids, 28 heptagons
 * edges = 98+98+196+196
 * vertices = 196
 * verf = Mirror-symmetric octahedron
 * symmetry = I2(7)≀S2, order 392
 * coxeter = xo7xx ox7xx&#zy
 * army=Hedep
 * reg=Hedep
 * custom_measure = (based on two heptagonal-tetradecagonal duoprisms of edge length 1)
 * el = Edges of duoprisms (98+98+196): 1
 * el2 = Lacing edges (196): $$\frac{\sqrt2}{2\sin\rac\pi7} ≈ 1.62971$$
 * circum = \frac{\sqrt{\frac{1}{\sin^2\frac\pi7}+\frac{1}{\sin^2\frac{\pi}{14}}}}{2} ≈ 2.52525
 * dual=Heptagonal duoexpandotegum
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+{\tan\frac{\pi}{14}}\sqrt{3+4\cos\frac{\pi}{7}}}$$ ≈ 1:1.26060.