Topology: "A branch of mathematics concerned with those
properties of geometric configurations which are unaltered by
elastic deformations (as stretching or twisting) that are
homeomorphisms."

This gallery contains four sculptures that investigate the
phenomenon of topology.  A simple example of topological
shape is the Mobius strip; a one sided strip of paper,
twisted 180 degrees at one end and reconnected so that it
has only one edge and one surface.

The largest sculpture, "Double Knot", has only one edge
and a single surface (i.e. both sides meet at some point).

"Duality", the next largest piece, has two separate edges,
each of which form single edge areas and then they intertwine
forming a single surface with two edges.

"Black Hole" plays with the two different ways that one can draw
a seven-point star.  The two figures are interlaced and then they
are placed in a stretched surface, like a rubber sheet or bubble.
This has to do with the warpage of space caused by gravity.

"Star Cinder" has ten separate edges and a single surface.


"Star Cinder" represents an imploded or collapsed star.
It also represents the opposite of "Eclipse" in the Hyatt Regency Hotel,
San Francisco.  While "Eclipse" is an exploding geometric form,
"Star Cinder" is an imploded one.

"Eclipse" starts, in its inner layer, as a pentagonal dodecahedron
(12 pentagons) and each face then rotates outward to the left.
At the midpoint it forms an icosadodecahedron (12 pentagons and 20 triangles).
What has happened is that the 12 pentagons have rotated outward
and equally apart and have formed 20 triangles between them.
Now the 12 pentagons continue to rotate outward to form another
figure called the "small rhombicosidodecahedron".  If the figure
were to continue to expand, rotating outward, it would form a whole
series of figures called Buckminsterfullerenes.  First would be the
figure with 20 hexagons and the 12 pentagons.

"Star Cinder" however has been imploded from the icosahedron,
a figure of 20 triangles; as these triangles rotate toward the center,
all in the same rotation, each pair of opposite triangles would eventually
meet in the center to form a figure of only 10 triangles.  For reasons
too long to explain here, I have chosen to round the apexes of these
triangles to connect them all with a single surface.

These two figures are using the scientific phenomena surrouding us
to speak of the gifts of our Universe.

THe mysteries of our Universe are our frontier.  Just as the caveman
portrayed his frontiers, so do we.