A
-dimensional
dual hyperoval can be regarded as the image
of a full
-dimensional projective
embedding
of a dual
circular space
. The
affine expansion
of
is a
semibiplane and its universal cover is the expansion of the abstract hull
of
.
In this paper we consider Huybrechts’s dual hyperoval, namely
where
is the dual of
the affine space
and
is induced by the embedding of the line grassmannian of
in
.
It is known that the universal cover of
is a truncation of a Coxeter
complex of type
and
that, if
is the codomain
of the abstract hull
of
, then
is a subgroup of
the Coxeter group
of type
,
but
is
non-commutative. This information does not explain what the structure of
is and how
is placed
inside
.
These questions will be answered in this paper.
|