According to wikipedia (but this is well known), A klee-Minty cube in $D$-dimension is defined by

$x_1\leq 5$

$4 x_1 + x_2 \leq 25$

$8 x_1 + 4 x_2 + x_3 \leq 125$

$16 x_1 + 8 x_2 + 4 x_3 + x_4 \leq 625\$

$32 x_1+ 16 x_2 + 8 x_3 + 4 x_4 + x_5 \leq 3125$

$\vdots \vdots$

$2^D x_1 + 2^{D-1} x_2 + 2^{D-2} x_3 + \ldots + 4 x_{D-1} + x_D \leq 5^D$

$x_1 \geq 0$

$x_2 \geq 0$

$x_3 \geq 0$

$x_4 \geq 0$

$x_5 \geq 0$

This poloyhedron has $2^D$ vertices. How can I find them. I have tried the following code

```
A= matrix(QQ, 10,5,[0,0,0,0,-1, 0,0,0,-1,-4, 0,0,-1,-4,-8, 0,-1,-4,-8,-16, -1,-4,-8,-16,-32,
1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1])
show(LatexExpr(r"\text{A = }"),A)
b=vector(QQ,[5,254,125,625,3125,0,0,0,0,0])
show(LatexExpr(r"\text{b = }"),b)
c=vector(QQ,[2^4,2^3,2^2,2^1,2^0])
show(LatexExpr(r"\text{c = }"),c)
AA=matrix(list(list([b])+list(transpose(A))))
show(transpose(AA))
pol = Polyhedron(ieqs = AA)
pol.Hrepresentation()
```

But I am far away from the account and some of the vertices are in the negative part of the hyperplan (which is impossible). Need some help to decipher my mistake. Thanks