Calculations at a right regular bifrustum. This is a regular frustum with an identical mirrored frustum attached to its large base.
Enter both side lengths a and b, a height h or H and the number of vertices of the bases. Choose the number of decimal places, then click Calculate. The half height h is the height of the original frustum.
Formulas:
H = 2 * h
L = 1/2 * n * ( a + b ) * √ cot²( π/n ) * ( a - b )² + 4h²
A = L + n * b² / ( 2 * tan(π/n) )
V = n * h * ( a² - b² ) / ( 6 * tan(π/n) )
Lengths and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
A regular bifrustum has the same symmetry properties as a regular bipyramid. It has a plane of symmetry along the large base of each individual frustum. In addition, it has several more planes of symmetry, corresponding to the number of vertices at the large base. If a large base has an odd number of vertices, these planes of symmetry pass through one vertex of the large base, the center of the opposite edge and the same way at both small bases, with parallel edges and the corresponding vertices. If a base has an even number of vertices, these planes of symmetry pass through two opposite vertices or edges of the large base and the according vertices or edges of the small bases.
This shape is also rotationally symmetric about an axis through the centers of both small bases at an angle of 360 degrees divided by the number of vertices at a large base. There are also additional horizontal axes of rotation, corresponding to the number of vertices at a large base. For an odd-numbered large base, these axes pass through a side vertex and the opposite edge. For an even-numbered large base, they pass through opposite corners or edges. The rotation angle for these axes is 180 degrees and multiples thereof.
In the case of an even number of large base vertices, this shape is point-symmetric about its center.
