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A star prism is a nonconvex polyhedron constructed by two identical star polygon faces on the top and bottom, being parallel and offset by a distance and connected by rectangular faces. A uniform star prism will have Schläfli symbol {p/q} × { }, with p rectangles and 2 {p/q} faces. It is topologically identical to a p-gonal prism.
Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space
Given that A is the area of the triangular prism's base, and the three heights h 1, h 2, and h 3, its volume can be determined in the following formula: [14] (+ +). Schönhardt polyhedron This way, one of its bases rotates around the prism's centerline and breaks the square faces into skew polygons .
Oblique rhombic prism: it has two rhombic faces, ... A formula to compute the volume of an n-parallelotope P in , whose n + 1 vertices are ,, ...
The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal prism with edges h the formula is (+)
The volume is found by taking the area of the base, with a side length of ... This formula also works for the oblique prism due to the Cavalieri's principle.
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).