Cut Cuboid Calculator

Name: Cut Cuboid - Geometry Calculator
Author: Jürgen Kummer

Calculations in a cut cuboid, a cuboid with a corner cut off. Thereby the edges a, b and c, which met at the cutt-off corner, were shortened to a₁, b₁ and c₁. The cut-off edge parts are a₂, b₂ and c₂.
Enter two lengths a, two heights b and two widths c. Choose the number of decimal places, then click Calculate.

Formulas:

a = a_{1} + a_{2}

b = b_{1} + b_{2}

c = c_{1} + c_{2}

d = \sqrt{{a_{2}}^{2} + {b_{2}}^{2}}

e = \sqrt{{b_{2}}^{2} + {c_{2}}^{2}}

f = \sqrt{{c_{2}}^{2} + {a_{2}}^{2}}

A = 2 \cdot (a b + a c + b c) - \frac{a_{2} b_{2} + a_{2} c_{2} + b_{2} c_{2}}{2} + \sqrt{\frac{d + e + f}{2} \cdot (\frac{d + e + f}{2} - d) \cdot (\frac{d + e + f}{2} - e) \cdot (\frac{d + e + f}{2} - f)}

V = a b c - \frac{a_{2} b_{2} c_{2}}{6}

The lengths have a one-dimensional 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 newly formed triangular face is always an acute triangle, meaning all its angles are smaller than right angles. At the three newly formed vertices of the cuboid on the other hand, two obtuse angles and an acute angle on the side of the triangle meet.
The corner truncated from the cuboid is correctly called a trirectangular tetrahedron. If the three perpendicular edges of this piece are of equal length, then it is a cube corner, an isosceles right tetrahedron. It is called a tetrahedron, four-sided polyhedron, because these corners have four faces. The cut cuboid, with its seven straight faces, is a heptahedron.
If an edge, rather than a corner, is cut off a cuboid, the result if this is straight cut off is a truncated cuboid.

In practice, corners of cuboids are cut off if they are in the way. A straight cut is often the simplest way to remove such a corner, easier than rounding it off. The calculations for a straight cut are also significantly simpler.
Cutting off such corners can serve as a safety measure, preventing injuries and damage. Corners can also be cut off for reasons of fluid dynamics, to reduce turbulence in air or water.

↑ up