Polyhedral Blooms that Retain Symmetry

bloom

sphere

pot

polyhedron

Tetrahedron

This Demonstration shows 'blooms' produced from polyhedra data. We use absolute value of

n

∑

j=1

Exp(2πvertex(j).(x,y,z))/n

, where

n

is the number of vertices of chosen polyhedra and

vertex(j)

is the coordinate of vertex

j

, taking only those dot products for which

vertex(j).(x,y,z)>0

. In this way the symmetry of the polyhedron is retained. The projecting on the unit sphere is also given.