Cube Corner Calculator

Name: Cube Corner - Geometry Calculator
Author: Jürgen Kummer

Calculations for a corner of a cube that has been truncated by its three adjacent vertices. This solid is also called an isosceles right tetrahedron and is a special type of corner. The faces of a cube vertex are three isosceles right triangles with leg lengths a and hypotenuse length b, and one equilateral triangle with side length b. The three right angles are located each between two edges a. The angle between a and b is 45 degrees, between two edges b it is 60 degrees.
Enter one of the two lengths a and b and choose the number of decimal places. Then click Calculate.

Formeln:

b = \sqrt{2} \cdot a

h = \sqrt{\frac{a^{2}}{3}}

r_{i} = \frac{a}{3 + \sqrt{3}}

A = \frac{(3 + \sqrt{3}) \cdot a^{2}}{2}

V = \frac{a^{3}}{6}

Lengths 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.

Six identical cube corners can be used to construct a cube with edge length a. Conversely, a cube can be divided into six such vertices. A vertex can also be cut from a cuboid or from a cube in such a way that the cut does not pass through other vertices. This is the case, for example, with the truncated cube or hexahedron, from which eight vertices are truncated in such a way that a shape with edges of equal length is created. The edge length a of the truncated hexahedron corresponds to the hypotenuse length b of the cube corner.

The cube corner is rotationally symmetric at an angle of 120 degrees and multiples thereof about the axis of rotation through the vertex with the three right angles and the center of the opposite equilateral triangle. It is mirror-symmetric with respect to the three planes on which this line and one of the three acute vertices lie.

If you fit two identical cube corners together at their equilateral base, you get a right square double pyramid, a special octahedron with eight right angles.

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