One way to rigorously define the angle between planes is as the supplementary angle to the angle between normal vectors. 1. Translate the condition that two dots in the Coxeter graph of a kaleidoscope are connected by an edge with label n into a condition on the inner product between their unit normal vectors. 2. Use this calculation to show find the graphs corresponding to the following kaleidoscopes: the kaleidoscope attached to the sphere which you found in 01 the D, kaleidoscope defined by the hyperplanes in R" with equations x1 - x2 = 0, X2 x3 = 0,X3 X4 = 0, ... , Xn-1 x, = 0, xn-1 + x, = 0. Thus, the realization of the kaleidoscope for a given graph depends on finding sets of linearly independent vectors with certain inner products. The standard method for proving that a kaleidoscope can't be realized is to show that if such a set existed, there would be a non-zero vector with zero or negative inner product with itself. 3. Apply this technique for the following Coxeter graphs: the graph corresponding to the Schfli symbol (4,4} the graph One way to rigorously define the angle between planes is as the supplementary angle to the angle between normal vectors. 1. Translate the condition that two dots in the Coxeter graph of a kaleidoscope are connected by an edge with label n into a condition on the inner product between their unit normal vectors. 2. Use this calculation to show find the graphs corresponding to the following kaleidoscopes: the kaleidoscope attached to the sphere which you found in 01 the D, kaleidoscope defined by the hyperplanes in R" with equations x1 - x2 = 0, X2 x3 = 0,X3 X4 = 0, ... , Xn-1 x, = 0, xn-1 + x, = 0. Thus, the realization of the kaleidoscope for a given graph depends on finding sets of linearly independent vectors with certain inner products. The standard method for proving that a kaleidoscope can't be realized is to show that if such a set existed, there would be a non-zero vector with zero or negative inner product with itself. 3. Apply this technique for the following Coxeter graphs: the graph corresponding to the Schfli symbol (4,4} the graph