Graphs on the Ceilings of Gothic Churches in Slovenia
Tomaz Pisanski
Univerza v Ljubljani, Slovenia
November 7,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Ceilings of Gothic churches containing ribbed vaults present
interesting mathematical patterns. A ribbed vault is a framework of
diagonal arched ribs carrying the cells which cover ceiling
in the spaces between them. Such a structure can be represented
as a graph on a surface or as a tiling of a plane. The bosses and
columns are vertices, the ribbed arches are edges and the cells
are faces of the embedded graph. Although such geometric patterns
can be found in Gothic churches throughout Europe we present some
special masterpieces of star vault networks from the ceilings of
late Gothic churches in Slovenia. In some cases the complicated
structure of such patterns can be explained by applying some
transformations that turn simple small graphs into
larger, more complicated ones. In most cases it is sufficient
to use the transformations that can produce from the graph of
tetrahedron successively the graphs of all other four Platonic
and the thirteen Archimedean solids. By combining simple
transformations into more complicated ones an interesting tool
for investigating maps on surfaces, tilings and polyhedra is obtained.
For instance, one of the composed transformations is known
in theoretical chemistry under the name of leapfrog
transformation.

Speaker's Contact Info: Tomaz.Pisankski(atsign)fmf.unili.si
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