Cross Cylinder Calculator

Name: Cross Cylinder - Geometry Calculator
Author: Jürgen Kummer

Calculations at a cross cylinder. Such a shape can be formed from a right circular cylinder with twice the height of its radius. In this cylinder, the diameter and height are equal, so it fits exactly inside a corresponding cube. If such a cylinder is bisected at its bases, creating two half-cylinders, each half-cylinder will have a square as a newly formed face. If one of these half-cylinders is then rotated 90 degrees so that the squares are again identical, and the two halves are joined together, a cross cylinder is formed.
The cross cylinder consists of two interlocking faces, each of which, when unfolded, has the shape of a stadium. Their length is the side length l of the cross cylinder. This shape has only one edge, a closed space curve, with the length of the circumference of the two circles of the cylinder.
Enter one value, choose the number of decimal places, then click Calculate.

Formulas:

l = (1 + \frac{π}{2}) \cdot a

m = 2 \cdot π \cdot a

A = \frac{3}{2} \cdot π \cdot a^{2}

V = \frac{π}{4} \cdot a^{3}

pi:

π = 3.141592653589793...

Diameter and lengths have the same unit (e.g. meter), as well as height and radius of the original cylinder. 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.

This very special shape is easy to calculate, as it has the same surface area and volume as a corresponding cylinder. However, manufacturing such a shape industrially in one piece is more difficult than manufacturing a cylinder, as it requires four-axis machining and cannot simply be milled like a cylinder. Perhaps this is why it is rarely used and can be considered a geometric exotic. Special dice have this shape. These can land on four different faces, even though the shape geometrically only has two. However, dice with four possible landing positions are usually tetrahedral.

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