Hollow Pyramid Calculator

Calculations at a right regular hollow pyramid. Here, a hollow pyramid is a regular pyramid, of which another regular pyramid with the same base and lesser height is removed at its base. The hollow pyramid is concave.
Enter side length, number of vertices of the base and two of the three heights. Choose the number of decimal places, then click Calculate.

	Edge length n-gon (a):			2n faces, 3n edges, n+2 vertices Example: pentagonal hollow pyramid Faces: 2n isosceles triangles, two different kinds
	Base vertices (n):
	Total height (h):
	Inner height (i):
	Missing height (j):
	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 hollow pyramids have the same symmetry properties as the corresponding regular pyramids. They are mirror-symmetric about every plane passing through a vertex or edge of the original base, through the directly opposite vertex or edge of the base, and through the apex. This original base is no longer a part of the hollow pyramid. There are as many planes of symmetry as there are vertices or edges at the base; this number is denoted here as n. These hollow pyramids are rotationally symmetric about an axis through the apex and the center of the base at an angle of 360 degrees divided by the number of vertices at the base.

The lengths of the slanted edges can be determined using the calculator for the regular pyramid, with the corresponding number of vertices, the side length a and the height h or j.

Last updated on 03/30/2026. Author: Jürgen Kummer

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