Univalent functions in the disc whose image is a particular eight-sided polygonal region determined by two parameters are studied. Whether such a function is Bazilevič is determined in terms of the two parameters, and the set of real
α
\alpha
’s is specified such that the function is
(
α
,
β
)
(\alpha ,\beta )
Bazilevič for some
β
\beta
. For any interval
[
a
,
b
]
\left [ {a,b} \right ]
where
1
>
a
⩽
3
⩽
b
1 > a \leqslant 3 \leqslant b
, a function of this type which is
(
α
,
0
)
(\alpha ,0)
Bazilevič precisely when
α
\alpha
is in this interval is found. Examples are given of non-Bazilevič functions with polygonal images and Bazilevič functions which are
(
α
,
0
)
(\alpha ,0)
Bazilevič for a single value
α
\alpha
.