Calculations at a corner, which has been straight cut off of a cube or cuboid. This solid is also known as trirectangular tetrahedron. At the vertex abc are three right angles.
Enter the three lengths a, b and c and choose the number of decimal places. Then click Calculate.
The height h is the distance between the vertex at abc and the base at def. 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.
The three mutually perpendicular edges of a trirectangular tetrahedron can have different lengths. If all three edges are the same length, then this shape is a cube corner. Such cube corners divide a corresponding cube into six exactly equal parts. Similarly, a cuboid can be divided with trirectangular tetrahedra into six parts, but these are not all congruent. In fact, two different types of corners are created in this process, each with three equal corners, which are mirror images of each other, i.e., left-handed and right-handed corners. This property is called chirality. The two different types of corners have the same volume and surface area, but the arrangement of the edges is reversed. The lengths of the perpendicular edges of these corners are the edge lengths of the cuboid. The other three edges of the trirectangular tetrahedron correspond to diagonals of the cuboid, two of which are face diagonals and one, the longest, is the space diagonal. Cuboids have three different types of face diagonals, but only one type of space diagonal.
The trirectangular tetrahedron appears in de Gua's theorem, which is the three-dimensional extension of the Pythagorean theorem: If three right angles meet at a vertex of a tetrahedron, then the sum of the squares of the areas of the three right triangles is exactly equal to the square of the area of the large intersection face.
For this corner, therefore