![]() ![]() This can be more clearly seen by referring to Figure 1.įigure 2 shows the general appearance of the r.d. The cube vertices are the short axis points, In Figure 2 below, the vertices of the octahedron are the long axis vertices ofĮach face, in this case N and J. Of course these axes do not actually appear on theįace of the polyhedron, I use them here for illustration. Because each face is a parallelogram, there are 2ĭistinct angles for each face, one which is bisected by the long axis, with anĪngle less than 90 degrees, the other bisected by the short axis, with an angle Semi-regular polyhedron, in that all of its edges are the same length, yet theĪngles of its faces differ. The rhombic dodecahedron (hereinafter, referred to as r.d.) is a It is important to understand that the outer vertices of the rhombicĭodecahedron form an octahedron, as this will be an important part of the Note also that the short axis segments (that is, That the edges of the octahedron bisect the diamond faces of the rhombicĭodecahedron upon their long axis (for example, NK bisects the long axis of theįace NEKF at the upper left). Octahedron, the most visible of which are NJ, NK, NL, MK, MJ, ML. You may perceive 3 edges of the cube in this drawing, which connect the top andīottom planes that is, FB,GC, HD and also some of the edges of the In Figure 1, I have marked the top and bottom planes of the cube in light gray,Īnd the square plane which serves as the base for the 2 face-bonded pyramids of ![]() We will, in the course of thisĪnalysis, find the diameter and radius of each of these spheres. Unlike the 5 regular solids, therefore, not all of the vertices of the rhombicĭodecahedron will touch one sphere. It is possible to draw a sphere around the cube, and another, (ABCD-EFGH), and the other 6 on the outside which form an octahedron The rhombic dodecahedron has 8 vertices in the middle that form a cube, Other words, they are square-sided figures with opposite edges parallel to one The faces are called rhombuses, because they are equilateral parallelograms. Notice in Figures 1 and 1A that the rhombic dodecahedron is composed of It has 12 faces, 14 vertices, 24 sides or edges.įigure 1A is Figure 1 slightly rotated, showing the edges of rhombicĭodecahedron (yellow), octahedron (green) and cube (blue). Prominently in Buckminster Fuller's Synergetics. The rhombic dodecahedron is a very interesting polyhedron. ![]()
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