Abstract
We study nodal complete intersection threefolds of type (2, 4) in
$${\mathbb {P}}^5$$
P
5
which contain an Enriques surface in its Fano embedding. We completely determine Calabi–Yau birational models of a generic such threefold. These models have Hodge numbers
$$h^{11}=2,h^{12}=32$$
h
11
=
2
,
h
12
=
32
. We also describe Calabi–Yau varieties with Hodge numbers
$$(h^{11},h^{12})$$
(
h
11
,
h
12
)
equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.