  Multidimensional diagonal-norm summation-by-parts (SBP) operators with
collocated volume and facet nodes, known as diagonal-$ \mathsf{E} $ operators,
are attractive for entropy-stable discretizations from an efficiency
standpoint. However, there is a limited number of such operators, and those
currently in existence often have a relatively high node count for a given
polynomial order due to a scarcity of suitable quadrature rules. We present
several new symmetric positive-weight quadrature rules on triangles and
tetrahedra that are suitable for construction of diagonal-$ \mathsf{E} $ SBP
operators. For triangles, quadrature rules of degree one through twenty with
facet nodes that correspond to the Legendre-Gauss-Lobatto (LGL) and
Legendre-Gauss (LG) quadrature rules are derived. For tetrahedra, quadrature
rules of degree one through ten are presented along with the corresponding
facet quadrature rules. All of the quadrature rules are provided in a
supplementary data repository. The quadrature rules are used to construct novel
SBP diagonal-$ \mathsf{E} $ operators, whose accuracy and maximum timestep
restrictions are studied numerically.
