1 Leonardo Da Vinci’s Vitruvian Man (1490) Canon of Properties Symmetry, Art & Science 4. Symmetry & Group Theory often used as an implied symbol of the essential symmetry of the human body, and by extension, to the universe as a whole. 4. Symmetry & Group Theory Symmetry & Nature
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4. Symmetry & Group Theory Symmetry, Art & Science 4a.pdf · 1 Leonardo Da Vinci’s Vitruvian Man (1490) Canon of Properties Symmetry, Art & Science 4. Symmetry & Group Theory often
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Leonardo Da Vinci’sVitruvian Man (1490)Canon of Properties
Symmetry, Art & Science
4. Symmetry &Group Theory
often used as an implied symbol of the essential symmetryof the human body, and by extension, to the universe as a whole.
3Vertices per face5Faces per vertex12Vertices30Edges20FacestriangleFace polygonPlatonicType
The Icosahedron
Connecting the centers of all the pairs of adjacent faces of any platonic solid produces another (smaller) platonic solid. The number of faces and vertices is interchanged, while the number of edges of the two is the same.
3Vertices per face5Faces per vertex12Vertices30Edges20FacestriangleFace polygonPlatonicType
total # ofsymmetry operations!
4. Symmetry &Group Theory
regular, convexProperties
icosahedronDual polyhedron
icosahedral (Ih)order 120Symmetry group
5Vertices per face
3Faces per vertex
20Vertices
30Edges
12Faces
pentagonFace polygon
PlatonicType
The Dodecahedron
Despite appearances, when a dodecahedron is inscribed in a sphere, it occupies more of the sphere's volume (66.49%) than an icosahedroninscribed in the same sphere (60.54%).