A bounded polytope given by its vertices, parametrised by convex
combinations of them; e.g. the plurality region
\(\{\theta : \theta_1 \le \theta_j\}\)
in the standard simplex. Use simplex_region() when the vertices are
affinely independent. cells() triangulates a polytope into simplices,
which is what certify() works on.
Usage
polytope_region(vertices = NULL, .hv = NULL)
Arguments
- vertices
(V, d) numeric matrix, one vertex per row.
- .hv
Internal only: the underlying dual-representation record in both
double and rational representation.
Value
A polytope_region, which is also a polyhedron_region() with
empty ray and lineality blocks.
Examples
# A square in R^2
polytope_region(vertices = rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)))
#> <polytope_region>
#> 4 vertices in R^2
#> facets: 4 inequalities
#> vertices:
#> [,1] [,2]
#> [1,] 0 0
#> [2,] 1 0
#> [3,] 1 1
#> [4,] 0 1