
...a folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the perimeter of the polygon together to form a polyhedron...focus on a specic type of at 2foldings, at 2foldings that wrap q; that is, foldings of p that cover both sides of q exactly once. we determine...

...plane, we consider the problem of finding a placement ϕc
1 of c
1 that minimizes the area of the convex hull of ϕc
1 ∪ c
2. we first consider the case...in time o(ε
− 1/2 log n + ε
− 3/2 log ε
− 1/2), if two sets are convex polygons with n vertices in total...

...show that for any open convex polygon p, there is a constant k(p) such that any k(p)fold covering of the plane with translates of p can be decomposed into...

...this paper proves the existence of nonperiodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons. for anyn?3...

...efficient quadratures for the integration of polynomials over irregular convex polygons and polyhedrons based
on moment fitting equations. the quadrature construction scheme involves the integration of monomial basis functions, which
is performed using homogeneous quadratures with minimal number of integration points, and the solution of a small linear system
of equations. the construction of homogeneous quadratures is based on...

...we show that any kfold covering using translates of an arbitrary convex polygon can be decomposed into ω...

...domain and denote by $${w^{2,2}_{\text{iso}}(s; \mathbb{r}^3)}$$ the set of mappings $${u\in w^{2,2}(s;\mathbb{r}^3)}$$ which...prove that the strong w
2,2 closure of $${w^{2,2}_{\text{iso}}(s; \mathbb{r...

...a band is the intersection of the surface of a convex polyhedron with the space between...does not contain any vertices of the polyhedron. the intersection of the planes and the polyhedron produces two convex polygons. if one of these polygons contains the other in the...

...edge flexagon made from irregular convex polygons. only a limited range
of irregular polygons leads to irregular polygon edge flexagons whose paper models...derived by replacing the regular convex polygons in a precursor regular polygon
edge flexagon by appropriate irregular convex polygons. the characteristic flex for an irregular polygon edge flexagon is
the same...

...original approach for the computation of the minkowski sum of a nonconvex polyhedron without fold and a convex polyhedron, without decomposition and union...first, we generate a superset of the minkowski sum facets using the concept of contributing vertices we accommodate for a nonconvexconvex pair of polyhedra. the generated superset guarantees...