  We study the implications of the simplicity constraint in the spincube model
of quantum gravity. By relating the edge-lengths to the integer areas of
triangles, the simplicity constraint imposes very strong restrictions between
them, ultimately leading to a requirement that all 4-simplices in the
triangulation must be almost mutually identical. As a surprising and unexpected
consequence of this property, one can obtain the CDT state sum as a special
case of the spincube state sum. This relationship brings new insight into the
long-standing problem of the relationship between the spinfoam approach and the
CDT approach to quantum gravity. In particular, it turns out that the spincube
model contains properties of both approaches, providing a single unifying
framework for their analysis and comparison. In addition, the spincube state
sum also contains some other special cases, very similar but not equivalent to
the CDT state sum.
