Polyhedra Sigfrid G. Fregert, M.D., Ph. D Emeritus Professor, Lund University 

Address: Mellanvångsvägen 5, S223 55 Lund, Sweden
Email: sigfrid.fregert@bredband.net
Art . Polyhedra constructions, Truncation of
Platonic polyhedra.
Polyhedra: Definition, History, Nature & Science, Archaeology, Exhibitions, References
The
regular polyhedra; The Platonic solids
The
regular polyhedra acc. to Leonrdo
da Vinci
Tetrahedron. Four triangles.
Symbolized fire
Cube
(hexahedron). Six squares. Symbilized earth
Octahedron: Eight triangles.
Symbolized air
Dodecahedron: 12 pentagons.
Symbolized aether,i.e. the
universe with sun, planets and fixstars.
Icosahedron: 20 triangles.
Symbolized water
The great stellated dodecahedron with 12 pentagrams acc to Kepler and Poinsot
The great
dodecahedron with12 pentagons acc. to Poinsot. Euler´s theorem
not valid.
The great icosahedron
with 20 triangles acc. to Poinsot
Semiregular polyhedra
Archimedes´ 13 semiregular polyhedra
Five
semiregular polyhedra acc.
to Archimedes
Regular and semiregular polyhedra with the same edge
Nonregular polyhedra
Nonconvex polyhedra ( 1 , 2 )
Duals
Octahedron is the dual to
cube. Cube is dual to octahedron. Tetrahedron is dual to tetrahedron.
Dodecahedron is dual to icosahedron.Icosahedron
is dual to dodecahedron
Prisms and antiprisms
Prisms: Tri  to octagonal prisms, acc. to Kepler
Antiprisms: Trito octagonal antiprisms , acc to Poinsot
Combinations of regular polyhedrons ; Compound polyhedra
Combinations of regular polyhedra: Icosahedron /
dodecahedron, cube/ icosahedr
Combinations of regular polyhedra: Tetrahedron / octahedron ,
cube / tetrahedron , cube / octahedron
Stella octangula,two tetrahedra, acc. to Kepler
Combination of
the five Platonic solids
Rhombic polyhedra
Rhombtricontahedron and rhombdodecahedron
Rhombic tricontahedron
and its derivatives
Closest packing of polyhedra
Closest packing of truncated octahedra
Closest packing of rhombic
dodecahedra
Closest packing of 13 spheres
in an icosahedron
Closest packing of 12 spheres
in a cuboctahedron
Divided polyhedra (Edge = E)
Hexahedron
(Cube) ( 1, 2, 3, 4, 5, 6, 7 )
Tetrahedron
of spheres ( 1, 2, 3)
Del3.htm Polyhedra
in nature and science
Bee´s cells, rhombic
dodecahedra with hexagonal openings
Rhombic dodecahedron.The
structure of bee´s cells, pomegranate pips and garnet
crystals.
Protein virus as icosahedra, twins and single
Poliovirus. Combination of icosahedron and dodecahedron
Polyhedra in beer foam to
save space
Truncated icosahedron. C60
fullerene,12 pentaons,20 hexagons.
Truncated icosahedronsoccerball
Last
modified on 13 januari 200120051115