please help

Consider the cube in the usual coordinates with the vertices at (:1, :1, :1). 1. Choose of a flag consisting of a vertex, edge and face of this polyhedron. Find the hyperplanes in the kaleidoscope corresponding to this choice. and the inequalities defining the triangle A on the unit sphere we've drawn to geometrically describe this kaleidoscope (touching the vertex, edge and face you chose). Also, find formulas for the reflections in these hyperplanes (hint: you can use the formula 35 - FE >> n-n P1 R(3c')=5c'2 where H is any normal vector to the plane but this probably unnecessarily complicated). 2. Calling these reflections in these planes R1, R2 , R3, find the order of the rotations R1R2 , R1 R3 , R2 R3. Describe these rotations geometrically. 3. Consider a point 35 = (x, y, z) in the triangle A (or on a ray through this triangle; being on the unit sphere doesn't have a special role). For each pair (1', j) = (1, 2), (1, 3), (2, 3), there is a polygon in a plane in R3 connecting 35 to R} to RiRJ-E to Rij Rf}, etc. until the loop closes. Taking for granted that this polygon is equiangular, for each of the options for (f, j) above, find the conditions (x, y, z) must satisfy in order for this polygon to be regular (including the case where some consecutive elements of the list are equal and so the number of edges drops). 4. Draw the Coxeter graph of this kaleidoscope, (hint: if you have trouble with this, do Q2 first) and for each way of circling 1, 2 or 3 vertices of this graph, find an example of a point 35 that gives the corresponding uniform polytope under the Wythoff construction, with faces given by the polygons from part 3 (you don't have to choose a point on the unit sphere)