dwarfcube(d)

description

                 
 

	This is a simple example of a dwarfed polytope. 
	The idea is that all but a small number of the vertices of 
	a cube are cut off by a single halfspace. The coordinates
	here are slighly wierd, so that the polar is nice for 
	building the family piercecube.  These polytopes
	are truncation polytopes.

keywords

simple, truncation polytope, dwarfed, facet-degenerate

references

11, 3

dim

d

uses

interval

n_facets

2d+1

n_vertices

d²+1

facets

ksum(H([-1/d,-1/d+3]), d) . h( 4, (-1) x d )

vertices

for ($i=1; $i<=$d; $i++){
   row( $d, (-1) x ($i-1), 3*$d-1, (-1) x ($d-$i) );

   for($j=$i+1; $j<= $d; $j++){
      row( $d, (-1) x ($i-1), 3*$d-1, 
		(-1) x ($j-$i-1), 2*$d-1, (-1) x ($d-$j) );
      row( $d, (-1) x ($i-1), 2*$d-1, 
		(-1) x ($j-$i-1), 3*$d-1, (-1) x ($d-$j) );
   }
}

row( $d, (-1) x $d );


returnmatrix();