simplex) can be looked at by finding the five vertices, and for each vertex, dropping the last Synergetics coordinate and plotting the resulting tetrahedron in three dimensional space, as follows.
The pentatope
(31) The triangle {1,1,1} can be looked at by finding the three vertices and plotting them in two dimensional space. The tetrahedron {1,1,1,1} can be looked at by finding the four vertices and plotting them in three dimensional space. {1,1,1,1,1}, (a simplex) can be looked at by finding the five vertices, and for each vertex, dropping the last Synergetics coordinate and plotting the resulting tetrahedron in three dimensional space, as follows.
Weisstein, Eric W. "Pentatope." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Pentatope.html
(32) The edge length of a four dimensional simplex such as {1,2,3,4,5} is just the sum of the five synergetics coordinates.
(33) For instance the 
simplex {1,2,3,4,5}.
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