  An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do
a short survey of their known properties and explain some new algorithms that
allow their efficient enumeration. Using this we give the symmetry groups of
all i-hedrites and the minimal representative for each. We also review the link
of 4-hedrites with knot theory and the classification of 4-hedrites with simple
central circuits. An i-self-hedrite is a self-dual plane graph with faces and
vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for
enumerating them based on i-hedrites. We give a classification of their
possible symmetry groups and a classification of 4-self-hedrites of symmetry T,
Td in terms of the Goldberg-Coxeter construction. Then we give a method for
enumerating 4-self-hedrites with simple zigzags.
