Abstract:

The attached PDFs explain further details of the methods used, as well as show actual color pictures of representative results by several authors, including some Alexander Grothendieck dessins d'enfants and A. Ocneanu's designed 3D-sculptures of 4D `shaddows' (actually special projections as described in the downloadable PDFs that are currently in the public dpomain). --------------------------------- ``The subject of the projection is a regular 4-dimensional solid of intermediate complexity, which Ocneanu calls an {\em ``octacube.''} It has 24 vertices, 96 edges and 96 triangular faces, which enclose 24 three-dimensional "rooms." Windows cut in faces allow the viewer to see within the structure, the same way that a window in a cubic room opens to the inside of the cube. Physically, the sculpture is a giant puzzle of 96 triangular pieces cut from stainless steel and bent into spherical shape''; (a quote attributed to the octacube's inventor, Professor Adrian Ocneanu). {\em Note:} The following, first document under Download is an example of a hand-drawn `mathematical diagram' by Alex Grothendieck around 1970 (perhaps a `dessin d'enfants' ? , or is it a 2D representattion of an $n$-dimensional real space by Alex's `doodle' drawing ?)

Rights:

Open access also: Copyright@1971 Alexander Grothendieck http://www.science.psu.edu/alert/math10-2005.htm http://www.ams.org/notices/200808/tx080800930p.pdf

Download:

AlxDudl.ppt
AlxDudl3.pdf
Aocnu4Dc.pdf
AOcnu_OctacubeFacts.pdf
AOcnub_4D.pdf
tx080800930p.pdf

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