(* To execute a command, click on it and press Shift+Enter *)

R = {{-1,0},{0,1}};   (* Define reflection matrix as a list of rows. Semicolon means don't display the result. *)

MatrixForm[R] (* Display matrix in table form *)

pts0={{-1,-1},{2,3},{3,2}}    (* Set of points in R^2, the corners of X0. Set and list both use {brackets}, not (parentheses). *)

polygon0=ConvexHullMesh[pts0]  (* Convex polygon with points as corners. A function uses [square brackets] *)

pts1=Table[ R.pts0[[i]],{i,1,Length[pts0]} ]  (* Compute symmetric points: pts0[[i]] = ith element of pts0 list; R.v = matrix mult *)

polygon1=ConvexHullMesh[pts1]  (* Symmetric polygon with points as corners. Also works for three-dimensional polyhedron. *)

polygon=RegionUnion[polygon0,polygon1];  (* Join the two polygons *)

Show[polygon]