Square pillar - Kakuchu

Given two parallel planes α and β, a line l intersecting them, and a polygon P on α, the part of the solid formed by all the lines passing through any point on P and parallel to l between α and β is called a rectangular prism (oblique prism). In this case, polygon P is called the base, and the faces that are not the base are called the sides. The distance between the two parallel planes α and β is called the height, and the volume of a rectangular prism with the area of ​​the base S and height h is V = Sh. Depending on whether the base is a triangle, a square, or a polygon, it is called a triangular prism, a rectangular prism, or a polygonal prism. A polygonal prism is also a solid formed by translating a polygon on plane α in the direction of the line intersecting α. A rectangular prism with a parallelogram as its base is called a parallelepiped. A parallelepiped can also be said to be a solid surrounded by three sets of two parallel planes. All of its faces are parallelograms. When the plane α and line l shown above are perpendicular to a rectangular prism, it is called a right prism, and a right prism with a regular polygonal base is called a regular prism. A right prism with a rectangular base is called a rectangular prism. A rectangular prism is a special case of a parallelepiped, and all of its faces are rectangular. In particular, a rectangular prism with all of its faces being square is called a cube.

[Minoru Kurita]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

平行な2平面α、βとそれらに交わる直線l、およびα上の多角形Pがあるとき、Pの任意の点を通ってlに平行な直線の全体のつくる立体のαとβの間にある部分を角柱（斜角柱）という。このとき、多角形Pを底面、底面でない面を側面という。また、平行2平面α、βの距離を高さといい、底面の面積がS、高さがhの角柱の体積はV＝Shである。底面が三角形、四角形、多角形であるのに応じて、三角柱、四角柱、多角柱という。多角柱はまた、平面α上の多角形がαに交わる直線の方向に平行移動してできる立体にもなっている。底面が平行四辺形の四角柱を平行六面体という。平行六面体は3組の平行な2平面で囲まれた立体ともいえる。その面はすべて平行四辺形である。角柱で、前に示した平面αと直線lが垂直のとき、これを直角柱といい、底面が正多角形の直角柱を正角柱という。底面が長方形の直角柱を直方体という。直方体は平行六面体の特殊な場合で、すべての面が長方形である。とくに、すべての面が正方形の場合の直方体を立方体という。

［栗田　稔］

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