Let
S
0
{S_0}
be an octic surface in
P
3
,
G
=
G
(
1
,
3
)
{{\mathbf {P}}^3},G = G(1,3)
= Grassmannian of lines in
P
3
{{\mathbf {P}}^3}
, and
J
=
{
(
x
,
l
)
|
x
∈
l
∩
S
0
}
⊂
S
0
×
G
{\mathbf {J}} = \{ (x,l)|x \in l \cap {S_0}\} \subset {S_0} \times G
. Then
dim
J
=
5
\dim {\mathbf {J}} = 5
. Let
L
=
{
l
|
l
is
e
v
e
r
y
w
h
e
r
e
tangent to
S
0
}
−
⊂
G
{\mathbf {L}} = {\{ l|l{\text { is }}everywhere{\text { tangent to }}{S_0}\} ^ - } \subset G
. Let
π
2
:
S
0
×
G
→
G
{\pi _2}:{S_0} \times G \to G
be the projection onto the second factor. We denote its restriction to
J
{\mathbf {J}}
also by
π
2
{\pi _2}
. Then the locus of everywhere tangent lines is
π
2
(
L
)
{\pi _2}({\mathbf {L}})
. In this article we show that the monodromy group of these lines is the full symmetric group.