This variant of the icosahedron has five kites meeting at each of its twelve vertices, forming what I call the twelve “kite-stars” of this polyhedron. Also, two kites meet at the midpoint of each of the icosahedron’s thirty edges. The emplacement of the kites changes the triangular faces of the icosahedron into equilateral, but non-equiangular, hexagons.
Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
The dodecagons are in the same planes as a cube’s faces, so there are six of them. Also, this could be constructed via an unusual truncation of the cube, using three different truncation-planes at each vertex. This polyhedron has thirty faces: the six dodecagons, and twenty-four kites (in eight sets of three).
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this polyhedron.
The kites to use have side lengths in a ratio of one to the square root of three, and angle measures of 60, 90, 120, and 90 degrees.
Because just about anyone can fly one kite at a time….
(Software credit: see http://www.software3d.com/stella.php)
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