1 Stellations, compounds, periodicity and the ... - Sandforsk

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4 Fig 3.1a The dodecahedron 3.1b The small stellated dodecahedron Change of constant to 3.3 gives the great dodecahedron in fig 3.2a And another change of constant to 2.5 gives the great stellated dodecahedron in fig 3.2b, another Kepler polyhedron of great beauty, and that also is on the cover of Wenninger’s famous book. Fig 3.2a The great dodecahedron 3.2b The great stellated dodecahedron 4 The icosahedron and some of its stellations First the icosahedron itself after equation 4.1, which is shown in fig 4.1a.
5 10 (t(x+y+z))10 +10 (t(-x+y+z))10 +10 (t(x+y-z))10 +10 (t(x-y+z))10 + 10 (x+t2 y) 10 +10 (-x+t2 y) 10 +10 (z+t2 x) 10 +10 (z-t2 x) 10 +10 (y+t2 z) 10 +10 (y-t2 z) 10 =10 6 4.1 † Using GD style in eq 4.2 we get the first stellation of the icosahedron fig 4.1b for a constant of 5, the second stellation for a constant of 4.5 in fig 4.2a, the great icosahedron for a constant of 3.5in fig 4.2b. 10 -(t(x+y+z))10 +10 -(t(-x+y+z))10 +10 -(t(x+y-z))10 +10 -(t(x-y+z))10 + 10 -(x+t2 y) 10 +10 -(-x+t2 y) 10 +10 -(z+t2 x) 10 +10 -(z-t2 x) 10 +10 -(y+t2 z) 10 +10 -(y-t2 z) 10 = const 4.2 † And using a constant of 2 we get the final stellation of the icosahedron. In this formidable periodicity in space there are 60 pikes, which is easy to find out from fig 4.3. Fig 4.1a The icosahedron 4.1 b First stellation of icosahedron Fig 4.2a Second stellation of icosahedron 4.2 b Great icosahedron
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1 Stellations, compounds, periodicity and the ... - Sandforsk

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