volumes of 4D polytopes ??
vdmcc
w.meeussen.vdmcc at vandemoortele.be
Thu May 6 17:37:29 CEST 1999
hi,
since every integer can be written as a sum of 4 squares in **at least**
one way,
every integer defines a 4D polytope.
Can volumes of such things be defined, and do they turn out to be integer
valued?
Does anyone have QHull (=C-program to calculate convex hulls in 4D) on
board?
ps.
of course the 3D equivalents (cfr earlier post) have volumes that are
Integer/3.
The proof is elementary. Eight octants. Each of'm with 3-fold axis.
Polytopes spanning across xy plane are cut in pieces by this plane, the new
(false) points lie on
existing ribs, colinear with the true vertices. Silly
w.meeussen.vdmcc at vandemoortele.be
tel +32 (0) 51 33 21 11
fax +32 (0) 51 33 21 75
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