Polyhedral organization of coronavirus?

Reimagining Coronavirus in 3D as a Metaphor of Global Society in Distress (Part #8)

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

Selected polyhedra with 72 vertices (wire frame versions shown below for each case)
1-Frequency Snub Dodecahedral Geodesic Sphere	3-Frequency Geodesic Octahedron (dual)	3 Truncated cubes	8+1 Cubes (dual)

Images generated with Stella Polyhedron Navigator

Exceptional polyhedra with both 72 vertices and 72 faces (with wire frame versions)
Small Stellated Dodecahedra 5+1	Small Stellated Dodecahedra 5+1 (wire)	Small Stellated Dodecahedra 5+1 (dual)	Small Stellated Dodecahedra 5+1 (dual)

Exceptional polyhedra with 74 vertices (with wire frame versions)
Stellated Cuboctahedron	Stellated Cuboctahedron (wire)	6-Frequency Tetrahedral Geodesic Sphere	6-Frequency Tetrahedral Geodesic Sphere (wire)
Images generated with Stella Polyhedron Navigator

The further step was then to explore the 3D variants of the polyhedra which variously corresponded to the assumed criteria of 72 vertices (or 74). As enumerated by Sergey Bederov, two were found possessing icosahedral symmetry. One of these, the pentakis snub dodecahedron, consists solely of triangles, but doesn't have mirror symmetry (namely it is chiral). The other is a polyhedron, seemingly without an official name (a "pentakis icosidodecahedron"?) has full icosahedral symmetry including mirror symmetry, but it also contains some squares in addition to triangles.

In the case of the 74-vertex polyhedra, none has icosahedral symmetry; the highest symmetry for these is cubic. Only one of them has approximately equal edges, and seemingly does not have an official name. In each case the polyhedral and mushroom-clouds models have been combined and variously adapted in the following which offers a sense of the distinctions between the vertices. Note that a further range of design options could be readily explored (colouring, motion rates, background, periodic peaking of mushroom-spikes, etc).

Global configuration of mushroom-clouds on vertices of polyhedra -- simulating a coronavirus
72 vertices -- icosahedral symmetry (mp4; x3d)		74 vertices -- cubic symmetry (mp4; x3d)
Animation of solid variant	Screen shot of wire frame variant	Animation of solid variant	Screen shot of wire frame variant
Combination and adaptation of polyhedral and mushroom-cloud models separately prepared by Sergey Bederov of Cortona3D

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]