Suppose v 1, ..........., v k are linearly independent vectors in R n (1 k
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Suppose v1,...........,vk are linearly independent vectors in Rn (1 ≤ k ≤ n). Then the set Xk = conv {±v1,.......,±vk} is called a k-cross polytope.
a. Sketch X1 and X2.
b. Determine the number of k-faces of the 3-dimensional cross polytope X3 for k = 0,1,2. What is another name for X3?
c. Determine the number of k-faces of the 4-dimensional cross polytope X4 for k = 0,1,2,3. Verify that your answer satisfies Euler’s formula.
d. Find a formula for fk(Xn), the number of k-faces of Xn, for 0 ≤ k ≤ n – 1.
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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