Descriptive Geometry
Assignment A3 2020/21/1

Given a dodecahedron derived from the cube ABCDEFGH as the figure shows. A line XY is also given; X is the common centre of the cube and the dodecahedron. Transforming XY into a projecting line, construct the image of the dodecahedron in the direction of XY. The 3^{rd} projection plane must be perpendicular to the 2^{nd} one. Show the visibility in system 12 and in system 34 of planes of projection. X(55, 130, 230); Y(95, 175, 277); b = 68. The edge length c of the cube and the edge length a of the dodecahedron are given by dividing b according to the golden ratio: b : c = c : a = (1 + sqrt5) / 2 = 1.618. The construction can be seen on the bottom of the figure. (Approaching c = 42, a = 26). The axes x_{12}, x_{23} and x_{34} are to be passed through the points X_{12}(0, 180), X_{23}(175, 277) and X_{34}(200, 115), respectively. 