Table 1 The f-vector for small BME polytopes.

4

2

(3,3)

5

5

(15, 105, 250, 210, 52)

6

9

(105, 5460, ?, ?, ?, 90262)

7

14

(945, 445410, ?, ?, ?, ?, ?)

ℬ

ℬ

ℬ

n

$\left(\begin{array}{c}n\\ 2\end{array}\right)$ - n

((2n - 5)!!,?, ...)