Regular Bipyramid Calculator

Calculations at a right regular bipyramid. This is a regular pyramid with its mirror image attached at its base.
Enter the side length, the height of one pyramid and the number of vertices of the base. Choose the number of decimal places, then click Calculate.

	Edge length n-gon (a):			2n faces, 3n edges, n+2 vertices Base in this example: square Joining faces: 2n isosceles triangles
	Base vertices (n):
	Height of one pyramid (h):
	Total height (i):
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Length 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.

The regular bipyramid is a special form of the general bipyramid. The bipyramid with the highest regularity has a square base and edges of equal length, this is an octahedron. The two Johnson bipyramids have somewhat less regularity.
Regular bipyramids have a plane of symmetry along the base of each individual pyramid. In addition, they have several more planes of symmetry, corresponding to the number of vertices at the base. If a base has an odd number of vertices, these planes of symmetry pass through both apexes of the bipyramid, one vertex of the base, and the center of the opposite edge. If a base has an even number of vertices, these planes of symmetry pass through both apexes of the bipyramid and two opposite vertices or edges of the base.
These shapes are also rotationally symmetric about an axis through both apexes at an angle of 360 degrees divided by the number of vertices at a base. There are also additional horizontal axes of rotation, corresponding to the number of vertices at a base. For an odd-numbered base, these axes pass through a side vertex and the opposite edge. For an even-numbered 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 corners, these shapes are point-symmetric about their center.

Calculation of volume and other dimensions: regular bipyramid

Last updated on 03/31/2026. Author: Jürgen Kummer

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