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Tag Archives: icosahedra
Augmenting the Icosahedron with Great Icosahedra
These two polyhedra are the icosahedron (left), and the great icosahedron (right). Since the faces of both of these polyhedra are equilateral triangles, it is possible to augment each of the icosahedron’s twenty faces with a great icosahedron. Here … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, geometry, great, icosahedra, isocahedron, Mathematics, polyhedra, polyhedron
1 Comment
An Icosahedron, Constructed from Smaller Polyhedra
The polyhedra at the vertices are rhombic triacontahedra, and the yellow edges are elongated rhombic prisms. This was made using Stella 4d, software you may try for free at this website.
Posted in Mathematics
Tagged geometry, icosahedra, Mathematics, polyhedra, polyhedron
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The Final Stellation of the Compound of Five Icosahedra
This was made using Stella 4d, software available at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged compound, final, five, geometry, icosahedra, Mathematics, polyhedra, polyhedron, stellate, stellated, stellation
1 Comment
A Rhombic Ring of Icosahedra, Leading to a Rhombic Dodecahedron Made of Icosahedra
As it turns out, eight icosahedra form this rhombic ring, by augmentation: Measured from the centers of these icosahedra, the long and short diagonal of this rhombus are in a (√2):1 ratio. How do I know this? Because that’s the … Continue reading
Posted in Mathematics
Tagged geometry, icosahedra, icosahedron, lattice, Mathematics, polyhedra, polyhedron, rhombic, rhombic dodecahedra, rhombic dodecahedron, rhombus, ring
2 Comments
A Rhombic Dodecahedral Lattice, Made of Icosahedra
I used Stella 4d: Polyhedron Navigator to make this. You can find this program at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged icosahedra, icosahedron, polyhedra, polyhedron, rhombic dodecahedron
2 Comments
Three Polyhedral Clusters of Icosahedra
In the last post on this blog, there were three images, and the first of these was a rotating icosahedron, rendered in three facecolors. After making it, I decided to see what I could build, using these tricolored icosahedra as … Continue reading
Posted in Mathematics
Tagged cluster, cube, geometry, icosahedra, icosahedron, Mathematics, polyhedra, polyhedron, tetrahedron
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On Icosahedra, and Pyritohedral Symmetry
In this icosahedron, the four blue faces are positioned in such a way as to demonstrate tetrahedral symmetry. The same is true of the four red faces. The remaining twelve faces demonstrate pyritohedral symmetry, which is much less wellknown. It … Continue reading
Posted in Mathematics
Tagged geometry, icosahedra, icosahedron, Mathematics, polyhedra, polyhedron, pyritohedral, pyritohedral symmetry, symmetry
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