Polyhedra
Ceramic models of polyhedra

Sigfrid G. Fregert, M.D., Ph. D

Emeritus Professor, Lund University

D

sigge.jpg (69105 bytes)

Address: Mellanvångsvägen 5, S-223 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 small stellated dodecahedron with 12 pentagrams acc. to Kepler and Poinsot. Euler´s theorem not valid.

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 semi-regular polyhedra

Five semiregular polyhedra acc. to Archimedes

Four semiregular polyhedra. Truncated cuboctahedron, icosidodecahedron, truncated icosahedron,truncated dodecahedron.

Four semiregular polyhedra. Snub cube, rhombicosidodecahedron, truncated icosidodecahedron, snub dodecahedro

Cuboctahedron

Regular and semi-regular polyhedra with the same edge

Non-regular polyhedra

Non-regular polyhedra

Non-convex 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 octa-gonal prisms, acc. to Kepler

Antiprisms: Tri-to octa-gonal antiprisms , acc to Poinsot

 

Combinations of regular polyhedrons ; Compound polyhedra

Combinations of regular polyhedra: Tetrahedron / octahedron, cube / tetrahedron, tetrahedron /icosahedron

Combinations of regular polyhedra: Tetrahedron / dodecahedron, octahedron / dodecahedron, dodecahedron / dodecahedron

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

Live Stella octangula

 

Rhombic polyhedra

Rhombtricontahedron and rhombdodecahedron

Four rhombic polyhedra

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)

Tetrahedron ( 1,  2 )

Hexahedron (Cube) ( 1,  2,  3, 4,  5,  6,  7 )

Octahedron ( 1,  2 )

Icosahedron

Dodecahedron

Cuboctahedron

Tetrahedron of spheres ( 1,  2,  3)

Del-3.htm Polyhedra in nature and science

Rhombic dodecahedron with 12 rhombi.(Diagonals 1/ Ö2) Rhombic tricontahedron with 30 rhombi (Diagonals 1/F)

Bee´s cells, rhombic dodecahedra with hexagonal openings

Rhombic dodecahedron.The structure of bee´s cells, pomegranate pips and garnet crystals.

Mineral crystal cubes

Protein virus as icosahedra, twins and single

Enzyme as rhomb dodecahedron

Radiolaria

Wasp´s net

Pomegranate pips

Poliovirus. Combination of icosahedron and dodecahedron

Polyhedra in beer foam to save space

Truncated icosahedron. C-60 fullerene,12 pentaons,20 hexagons.

Truncated icosahedron-soccerball

C-70 fullerene

Last modified on 13 januari 20012005-11-15