Example of a heptagonal polyhedron? I did a lot of googling but I'm unable to find an example of a convex polyhedron in 3-dimensional space, such that its faces are all congruent irregular heptagons. Is there a reason such a shape can't exist? Also in parallel what is the word for a polyhedron, such that all of its faces are congruent but not necessarily face-transitive.

$$ V - E + F = 2 $$ let's see, $$ E = 7 F / 2 $$ Each vertex meets at least three faces, $$ V \leq 7F / 3. $$ $$ V - E + F \leq \frac{7F}{3} - \frac{5F}{2} = \frac{-F}{6} $$ $$ V - E + F \leq \frac{-F}{6} $$ $$ 2 \leq \frac{-F}{6} $$ which is bad