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by Steven H. Cullinane

In finite geometry and combinatorics,
an inscape is a 4x4 array of square figures,
each figure picturing a subset of the overall 4x4 array:


Inscapes provide a way of picturing
the following equivalent concepts:

The 60 (= 15×4) Göpel tetrads in PG(3,2),

The generalized quadrangle GQ(2,2),

Tutte's 8-cage, and

the Cremona-Richmond 153 configuration (pdf):


Diamond Theory shows that this structure
can also be modeled by an inscape:


The illustration below shows how the
points and lines of the inscape may
be identified with those of the
Cremona-Richmond configuration.


Related material on inscapes:

Rosenhain and Göpel Tetrads in PG(3,2)

The 2-Subsets of a 6-Set are the Points of a PG(3,2)

A Symplectic Approach to the Miracle Octad Generator

Inscapes, Inscapes II, Inscapes III, Inscapes IV

Page created Jan. 19, 2006.  Last modified March 26, 2013.