Perspective of a regular octahedron by orthographic projection onto a plane parallel to a diagonal square of the solid. No letters to denote the points, but the hexagonal cross sections and the colors of the faces and edges are the same in this image, where notations exist. The same octahedron again is in this other image. The diagonal square with green sides is the outline of the solid, depicted with its true shape. It is easy to imagine the effect of a quarter turn around the diagonal of the solid, which is parallel to the sight direction. Whatever the sense of the rotation, one quarter turn around a diagonal of the octahedron transforms the octahedron into itself, and also preserves a cross section perpendicular to this diagonal.In front of the solid the altitudes of each face are three yellow lines. The orthocenter of a face is the center of a target, we imagine the two orange circles of the target painted on the face. The projection distorts the four targets and the twelve symbols of right angles at the feet of the altitudes. The projection also distorts a cross section of the solid parallel to two faces: a hexagon with white sides. The three consecutive sides of the hexagon behind the solid are dashed depicted. Each vertex of the hexagon is the midpoint of an edge of the solid. The three diagonal squares and the white hexagon are four cross sections passing through the center of the solid, that are four regular polygons.
Own work
Yves Baelde