  Geometrical frustration in thin sheets is ubiquitous across scales in biology
and becomes increasingly relevant in technology. Previous research identified
the origin of the frustration as the violation of Gauss's \emph{Theorema
Egregium}. Such "Gauss frustration" exhibits rich phenomenology; it may lead to
mechanical instabilities, anomalous mechanics and shape-morphing abilities that
can be harnessed in engineering systems. Here we report a new type of
geometrical frustration, one that is as general as Gauss frustration. We show
that its origin is the violation of Mainardi-Codazzi-Peterson compatibility
equations and that it appears in Euclidean sheets. Combining experiments,
simulations and theory, we study the specific case of a Euclidean ribbon with
radial and geodesic curvatures. Experiments, conducted using different
materials and techniques, reveal shape transitions, symmetry breaking and
spontaneous stress focusing. These observations are quantitatively rationalized
using analytic solutions and geometrical arguments. We expect this frustration
to play a significant role in natural and engineering systems, specifically in
slender 3D printed sheets.
