Bifrustum

{{Infobox polyhedron | name = Family of bifrusta | image = Hexagonal bifrustum.png | caption = Example: hexagonal bifrustum | type = | euler = | faces = -gons trapezoids | edges = | vertices = | vertex_config = | schläfli = | wythoff = | conway = | coxeter = | symmetry = | rotation_group = | surface_area = \begin{align} &n (a+b) \sqrt{\left(\tfrac{a-b}{2} \cot{\tfrac{\pi}{n}}\right)^2+h^2} \\[2pt] & \ \ +\ n \frac{b^2}{2 \tan{\frac{\pi}{n}}} \end{align} | volume = n \frac{a^2+b^2+ab}{6 \tan{\frac{\pi}{n}}}h | angle = | dual = Elongated bipyramids | properties = convex | vertex_figure = | net = | net_caption = }} In geometry, an -gonal bifrustum is a polyhedron composed of three parallel planes of -gons, with the middle plane largest and usually the top and bottom congruent. It can be constructed as two congruent frusta combined across a plane of symmetry, and also as a bipyramid with the two polar vertices truncated. They are duals to the family of elongated bipyramids.

{{Infobox polyhedron | name = Family of bifrusta | image = Hexagonal bifrustum.png | caption = Example: hexagonal bifrustum | type = | euler = | faces = -gons trapezoids | edges = | vertices = | vertex_config = | schläfli = | wythoff = | conway = | coxeter = | symmetry = | rotation_group = | surface_area = \begin{align} &n (a+b) \sqrt{\left(\tfrac{a-b}{2} \cot{\tfrac{\pi}{n}}\right)^2+h^2} \\[2pt] & \ \ +\ n \frac{b^2}{2 \tan{\frac{\pi}{n}}} \end{align} | volume = n \frac{a^2+b^2+ab}{6 \tan{\frac{\pi}{n}}}h | angle = | dual = Elongated bipyramids | properties = convex | vertex_figure = | net = | net_caption = }} In geometry, an -gonal bifrustum is a polyhedron composed of three parallel planes of -gons, with the middle plane largest and usually the top and bottom congruent. It can be constructed as two congruent frusta combined across a plane of symmetry, and also as a bipyramid with the two polar vertices truncated. They are duals to the family of elongated bipyramids. \begin{align} A_l &= n (a+b) \sqrt{\left(\tfrac{a-b}{2} \cot{\tfrac{\pi}{n}}\right)^2+h^2} \\[4pt] A &= A_l + n \frac{b^2}{2 \tan{\frac{\pi}{n}}} \\[4pt] V &= n \frac{a^2+b^2+ab}{6 \tan{\frac{\pi}{n}}}h \end{align} The volume V is twice the volume of a frustum.

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