== 4-simplex: f-vector (5, 10, 10, 5)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 5.4e-17
   (b) eigenvalues: 1 negative, 4 zero, 0 positive  (smallest -0.5; zero block max |.| 6.3e-17)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 3.7e-17 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [-0.1 -0.1 -0.1 -0.1 -0.1]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 1.1e-05
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== prism over tetrahedron: f-vector (8, 16, 14, 6)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 0.0e+00
   (b) eigenvalues: 1 negative, 4 zero, 3 positive  (smallest -0.01562; zero block max |.| 2.6e-18)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 0.0e+00 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 1.0e-02
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== 3-3 duoprism: f-vector (9, 18, 15, 6)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 5.9e-17
   (b) eigenvalues: 1 negative, 4 zero, 4 positive  (smallest -0.006173; zero block max |.| 1.1e-18)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 3.0e-17 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [0.0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0021]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 8.9e-03
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== cyclic C(6,4): f-vector (6, 15, 18, 9)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 5.3e-15
   (b) eigenvalues: 1 negative, 4 zero, 1 positive  (smallest -5.699e-05; zero block max |.| 1.8e-17)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 1.7e-15 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [-9.3528e-06 -5.8455e-06  5.1148e-06  5.1148e-06 -5.8455e-06 -9.3528e-06]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 1.4e-04
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== octahedral prism: f-vector (12, 30, 28, 10)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 6.2e-17
   (b) eigenvalues: 1 negative, 4 zero, 7 positive  (smallest -0.0003858; zero block max |.| 2.1e-19)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 3.1e-17 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002]
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== pyramid over octahedron: f-vector (7, 18, 20, 9)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 5.2e-16
   (b) eigenvalues: 1 negative, 4 zero, 2 positive  (smallest -0.01852; zero block max |.| 7.3e-18)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 2.5e-16 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [-1.5613e-19 -3.4694e-20 -1.5613e-19 -2.6455e-03 -3.9899e-19 -1.3878e-19 -3.9899e-19]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 5.0e-05
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
== non-symmetric 0/1 example: f-vector (7, 18, 20, 9)
   (M1) sign pattern = graph of Q: True;  (a) residual of 'sum_j M_ij v_j parallel to v_i': 2.2e-16
   (b) eigenvalues: 1 negative, 4 zero, 2 positive  (smallest -0.02811; zero block max |.| 4.9e-18)
   (c) relative residual of M * V = 0 (V = matrix of the vertices of Q): 1.0e-16 -> with corank 4 the kernel is exactly {(<v_i,p>)_i}
   (d) Strong Arnold Property: nullity of X -> MX on admissible X: 0
       diagonal entries M_ii: [ 5.9524e-03 -2.9762e-03 -2.9762e-03 -9.9127e-19 -9.9206e-04  1.9841e-03  1.9841e-03]
   (e) finite-difference Hessian of vol(P(x)) at x = 1: max |(-H) - M| / max |M| = 3.4e-03
   => Izmestiev's matrix for Q* has null-space representation i -> v_i (vertices of Q): True
ALL EXAMPLES: True
