Calculations at a cuboid with obtuse edges, a cuboid with regularly cut off edges. As surfaces, from the former rectangles smaller rectangles emerge and from the former edges rectangles with isosceles, right triangle attached at the ends emerge. The volume is calculated as the volume of the inner cuboid plus the elevation of the inner cuboid faces to the former cuboid plus the inclined filled gaps at the former edge to the lengths of the smaller rectangles plus twice the eight corners (corner to the inside and the outside each).
Enter one length, width and height each, of the former cuboid (a, b, c) or of the inner cuboid (a', b', c') and the cut width at the edges. The cut width is the distance between two newly emerged, parallel edges. Choose the number of decimal places, then click Calculate.
Formulas:
a' = a - √2 * t
b' = b - √2 * t
c' = c - √2 * t
d = √ a'² + b'² + c'² + 2 * √ t² / 6
A = 2 * [ a'b' + a'c' + b'c' + 2t*(a'+b'+c') + 3t² ]
V = a'b'c' + √2 * t * (a'b'+a'c'+b'c') + t² * (a'+b'+c') + 4/(3*√2)t³
Lengths, widths, heights and diagonal 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 formulas for calculating thsi shape are quite complicated, as this solid can be assembled from many individual parts, each of which is easier to calculate individually. The straight sides are three different rectangles, which appear in opposite pairs, making six rectangles in total. The slanted sides, created by cutting off the edges, are also three different ones, but there are four of each, making twelve in total. These are each isosceles hexagons with a right angle at both ends. The space diagonal is noticeably shorter than that of the original cuboid, as its former vertices have disappeared.
