This tiling set is readily obtained from a spherical icosahedron
(or from a spherical dodecahedron) by connecting the center of each spherical face to the vertices of the face with geodesics.
Thus an icosahedron
provides a lot of space for packaging the genome, entails simple assembly for the maximum space, and provides a sable home for the virus until the next round of infection.
It is worth to mention here that there are some recent articles discussing plausible theoretical links between icosahedron
model and close-packed model of nuclei entities, for instance by the virtue of Baxter theory .
In Figure 14, the parallel small circle projection is applied to the icosahedron
using Snyder's arrangement (1992).
In the score for Shifting Shapes, the dancers are tracing the periphery of the icosahedron
, just as Sarah Leddy did for Sapphire.
The direct connection between the 3-D and 4-D spaces is realized when one equates the 120 group operations on the regular icosahedron
(3, 5) to the vectors for the 120 vertices of the 600-cell hypericosahedron (3, 3, 5) in 4-D space in a particular way.
The motif that stood out time and again was a set of symmetries seen in various structures, including soccer balls, spherical geodesic domes, and the 20-sided, jewel-like shape known as the icosahedron
Among these the truncated icosahedron
has proved to be popular (White et al.
I leave the icosahedron
and dodecahedron as an exercise for the reader.
Just as the six pennies in dimension two sit at the comers of a regular hexagon, the 12 balls in dimension three also sit at the corners of a regular shape: an icosahedron
, which has 20 triangular sides.
Fekete and Treinish's (1990) spherical quadtree data structure, which is based on recursive subdivision of spherical triangles obtained by projecting the faces of an icosahedron
onto a sphere, is a good example of great-circle edge partitioning.
There he proves that the tetrahedron, the hexahedron (a cube), the octahedron, the dodecahedron, and the icosahedron
are the only possible regular convex solids (Fig.