4 problems

Consider a planar framework with $\mathcal{C}_{3v}$ symmetry, freedom number $k=0$, and $v_c=0$. If $e_{\sigma}=1$, then there are no symmetry-detectable self-stresses or mechanism…

Pinned rotational symmetry isostaticity conjecture. For rotational groups $\mathcal{C}_n$, $n>2$, in the plane, pinned $\mathcal{C}_n$-isostaticity is equivalent to pinned isostati…

Let a block and hole polyhedron $\mathcal{P}$ have cut cycles $\mathcal{C}$ of size $c$, and let $\mathcal{P}_{C}'$ denote each corresponding component, with block sizes $b_i'$ and…

Let a block and hole polyhedron $\widehat{\mathcal{P}}$ satisfy the separation conditions: two blocks and two holes intersect in at most two vertices, intersections in two vertices…