Re: The Platonic Solids
From Dave Bird---St Hippo of Augustine <dav...@xemu.demon.co.uk>
· alt.ascii-art
· 30 Jun 1997 00:00 · View full thread
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In article <33B...@math.fsu.edu>, Michael Naylor <mna...@math.fsu.edu> writes: This is a very nice little project. Is there a formula describing the number of faces, edges, and corners? One way to look at the lefthand column is: take an N-sided regular polygon, and N more such depending from each of its outside edges. Cutting this out, you can fold them down until they meet.... N=3 : in a point N=4 : in a similar N-sided face N=5 : an identical object placed below & rotated 1/(2N) of a circle N=6 : no figure possible because there is no gap between the six hexagons to be folded away. With a little patience, compasses, and a circular protractor, it is therefore not that hard to mark out a sheet of card so you can cut-out-and-fold into a dodecahedron. In the righthand column you swap verteces <-> faces i.e. start at a point (instead of an N-sided face) and conect it with N triangles to N surrounding points (instead on N similar N-sided faces). > > The Platonic Solids > > by Michael Naylor > > (best viewed in Monaco 9 point) > > . > /!;, > / `;;, > / !;;, > / `;;;;, > / !;;;;, > / `;;;;;) > / !;;;/ > ``--__ `:;/ > ``--_!/ > > Tetrahedron > .___________, ,;/\`_ > |\'.'.'.'.'.'\ ,;;/ \'`_ > |:\.'.'.'.'.'.\ ,;;;/ \.'`_ > |::\'.'.'.'.'.'\ ;;;;/ \'.'! > |:::+-----------+ Hexahedron Octahedron ;;;/ \.'! > |:::| | ;;/ \'! > |:::| | :/____________\; > \:::| | `-_ _- > \::| | `-_ _-' > \:| | `-_ _-' > \!___________! '-' > > Dodecahedron Icosahedron > > .----------,, > ,"__ _-:, ._. > / ""--_--""...:\ ,_-','.`-_ > / |.........\ ,_-' ,' `. `-_, > / |..........\ !' `-,-_______'-':: > /, _'_........./: ; / \ /.\::: > ! -, _-" "-_... ,;;: ! / \ /...\:: > \ -_-" "-_/;;;; ! / \ /.....\: > \ \ /;;;;' ;'--.._..\/_._..-;; > \ \ /;;;; '-_ :!;;;;;;' > '. \ /;;;' `-_, :!;;;' > "-_\_______/;;' `-!' mn @@@ @@@ @("} {")@ @(.(.)\__ __/(.).)@ @@@) ( """""""""""""""""""""""""""""""""" ) (@@@ ( . ) dav...@xemu.demon.co.uk ( . ) \ ) / http://www.xemu.demon.co.uk \ ( / \\.-' ,' /index.html ', `-_// // ~-~ """""""""""""""""""""""""""""""""""""""""" '~ \\ / \ "Consciousness is a product of the brain no more & no less than earwax is a product of the ear"-Martin Hunt on a.r.s
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,695e46d560235b56,start X-Google-Attributes: gidf996b,public From: Dave Bird---St Hippo of Augustine <dav...@xemu.demon.co.uk> Subject: Re: The Platonic Solids Date: 1997/06/30 Message-ID: <W3w...@xemu.demon.co.uk>#1/1 X-Deja-AN: 253799629 Distribution: world X-NNTP-Posting-Host: xemu.demon.co.uk [158.152.196.209] References: <33B...@math.fsu.edu> Organization: 1st Canine Chapel of Bob Dobbs Dog (Church of the SubGenius) Newsgroups: alt.ascii-art
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