Ugo Adriano Graziotti

                                                                          

During the years 1978-1994 I was in correspondence with Ugo Adriano Graziotti.
From him I received his beautiful book
'Polyhedra. The Realm of Geometric Beauty', San Francisco, 1962, illustrated.

On 6.6.1978 I received also two copies of his booklet
'Poliedri Sorgenti Inesauribili di Design', Castenedolo (BS), Settembre, 1977,
18 p., 30cm x 21cm, illustrated.
I do not understand the Italian language. Notwithstanding I get the impression
that like his first book the theory is not of decisive importance,
but the illustrations are of an artistic level, e.g. unfoldings of polyhedra.

On 2.4.1991 I received a book concerning his artistic work as a painter and a sculptor
and concerning his work as a mathematician:
'Adriano Graziotti a cura di Augusto Giordano', Studio Effe 76 s.r.l., Roma, 1986,
120 p., 31cm x 25 cm, illustrated.
On pages 83-110 there is a chapter 'Graziotti Matematico' with beautiful illustrations,
of which some are borrowed from the mentioned booklet. In this chapter as in the booklet
he treats some historical aspects on polyhedra.


                              "... the origin, development and natural geometric construction
                                      of the most important duals..."              (The Realm ... , p.3)


                                             Remark.       Images become visible after download.
                                                                      Some are quite large, so it can take some time.


Plate Ia : The origin of the Triakis Tetrahedron, the Triakis Octahedron and the
Triakis Icosahedron (See: The Realm ... , Plates I, II, IV).

Plate Ib : The origin of theTetrakis Hexahedron and the Pentakis Dodecahedron
(See: The Realm ... , Plates III, IX). At the left side I added three images illustrating
an alternative origin of the Triakis Tetrahedron.


Plate IIa : The origin of the Rhombic Dodecahedron and the Rhombic Triacontahedron
(See: The Realm ... , Plates VI, VII). At the left side I added three images illustrating the origin
of the Cube (the Rhombic Hexahedron) being the case of the Stella Octangula.

Plate IIb : The origin of the Rhombic Dodecahedron and of variants on the Deltoidal
Icositetrahedron and the Deltoidal Hexecontahedron (See: The Realm ... , Plates VI, V, X).


Plate IIIa : The origin of the Tetrakis Hexahedron, the Hexakis Octahedron
and the Hexakis Icosahedron (See: The Realm ... , Plates III, VIII, XI).

Plate IIIb : The origin of the Pentagonal Icositetrahedron and the Pentagonal Hexecontahedron
(See: The Realm ... , Plates XII, XIII). At the left side I added three images illustrating the origin
of the Dodecahedron.


Plate IV : Leonardo style polyhedra : compound of five Tetrahedra; solid starred Small
Rhombicosidodecahedron (Compare with : The Realm ... , Plate XI); compound of the
Icosahedron and the Dodecahedron; Graziotti in his studio.

Plate V : Unfoldings of polyhedra : the Snub Cube, the Rhombicosidodecahedron,
a variant on the compound of the Icosahedron and the Dodecahedron.

Plate VI : Polyhedral sculptures : sculpture deduced from the compound of five tetrahedra;
a geodesic dome.

Plate VII : An historical chart of polyhedra according to Graziotti;
the artist Adriano Graziotti (four images).


I recommend following Site on Ugo Adriano Graziotti :

http://g.casagrande.home.att.net/poliedri/poliedri.html


Links :

F and S Solids and their Compounds

Plates


http://mathworld.wolfram.com/ArchimedeanSolid.html

http://mathworld.wolfram.com/DualPolyhedron.html

http://mathworld.wolfram.com/CatalanSolid.html

http://mathworld.wolfram.com/Cumulation.html


http://www.georgehart.com/virtual-polyhedra/archimedean-duals-info.html

http://www.georgehart.com/virtual-polyhedra/duality.html