  The first results presented in our article are the clear definitions of both
intrinsic and extrinsic discrete curvatures in terms of holonomy and
plane-angle representation, a clear relation with their deficit angles, and
their clear geometrical interpretations in the first order discrete geometry.
The second results are the discrete version of Bianchi identity and
Gauss-Codazzi equation, together with their geometrical interpretations. It
turns out that the discrete Bianchi identity and Gauss-Codazzi equation, at
least in 3-dimension, could be derived from the dihedral angle formula of a
tetrahedron, while the dihedral angle relation itself is the spherical law of
cosine in disguise. Furthermore, the continuous infinitesimal curvature 2-form,
the standard Bianchi identity, and Gauss-Codazzi equation could be recovered in
the continuum limit.
