Non-Orientable Infinite
Polyhedron
Genus: 1
Symmetry: Linear
Unlike the rest of the models in
this series, this model is not regular at all but it's interesting
because
it's an example of a non-orientable
(i.e. one-sided) polyhedron. Because its genus is 1 it's related to the
Klein bottle which is the finite surface with the same genus. Like it's
finite cousin, it is a surface with only one side. The
green
neck on the left is attached to a hole in the red box next to it
creating
one repeat unit. The red box has a hole in one side where the neck of
the
next repeat unit attaches, etc. creating an infinite chain. That's why
you can see the interior of only the right-most box above. Since only
three
repeat
units are displayed here and the right-most unit is the only one
without
a neighboring neck attaching to it's side hole. Note that each neck
pokes
through it's neighbor box without interacting topologically with the
box
face it penetrates. The only interaction of a neck with a neighbor box
is where that neck joins with the neighbor box's side hole.
VRML 2 model.
Main Infinite Regular
Polyhedra page.
Superliminal home page.