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Note that with the cube (see image) the perimeter of the resulting 2D drawing is a perfect regular hexagon: all the black lines have equal length and all the cube's faces are the same area. Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation.
D 1h and C 2v: group of order 4 with a reflection in a plane and a 180° rotation through a line in that plane; D 1d and C 2h: group of order 4 with a reflection in a plane and a 180° rotation through a line perpendicular to that plane. S 2 is the group of order 2 with a single inversion (C i). "Equal" is meant here as the same up to conjugacy ...
A cross-section of a solid right circular cylinder extending between two bases is a disk if the cross-section is parallel to the cylinder's base, or an elliptic region (see diagram at right) if it is neither parallel nor perpendicular to the base. If the cutting plane is perpendicular to the base it consists of a rectangle (not shown) unless it ...
Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.
D 1h and C 2v: group of order 4 with a reflection in a plane and a 180° rotation about a line in that plane. D 1d and C 2h: group of order 4 with a reflection in a plane and a 180° rotation about a line perpendicular to that plane. For n = 2 there is not one main axis and two additional axes, but there are three equivalent ones.
This image line is perpendicular to every line of the plane which passes through the origin, in particular the original line (point of the projective plane). All lines that are perpendicular to the original line at the origin lie in the unique plane which is orthogonal to the original line, that is, the image plane under the association. Thus ...
Plane orthogonal to line L and including the origin. Point B is the origin. Line L passes through point D and is orthogonal to the plane of the picture. The two planes pass through CD and DE and are both orthogonal to the plane of the picture.
Other models of hyperbolic space can be thought of as map projections of S +: the Beltrami–Klein model is the projection of S + through the origin onto a plane perpendicular to a vector from the origin to specific point in S + analogous to the gnomonic projection of the sphere; the Poincaré disk model is a projection of S + through a point ...