Johnson Pyramids Calculator

Name: Johnson Pyramids: Square and Pentagonal Pyramid - Geometry Calculator
Author: Jürgen Kummer

Calculations with Johnson pyramids. Johnson solids are convex polyhedra with regular polygon faces, that are not Platonic or Archimedean solids, prisms or antiprisms. Square (J₁) and pentagonal (J₂) pyramid are the first two of the 92 Johnson solids.
Enter the type of pyramid and one value and choose the number of decimal places. Then click Calculate.

Length and height 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. See also square pyramid, regular pyramid.

The Johnson solids were first listed by Norman Johnson in 1966. In 1969 it was proven that they complement the Platonic and Archimedean solids, as well as prisms and antiprisms, in such a way that no other polyhedra exist that have exclusively regular polygons as side surfaces. Not all Johnson solids can be calculated on these pages, only the most important ones, although this selection is of course subjective. On some pages multiple related Johnson solids can be calculated, such as the two pyramids here made up of four and five equilateral triangles. Six equilateral triangles next to one another form a regular hexagon, i.e. not a polyhedron, but a polygon. More than one Johnson solid per side can be found in the cupolae, elongated pyramids, gyroelongated pyramids, Johnson bipyramids and the elongated bipyramids. This means that 22 of the 92 different Johnson solids can be calculated here; for the others, please refer to the relevant specialist literature. Unfortunately, for many of them the corresponding formulas are difficult to find.

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