sagemathgh-39389: minor detail in combin. polyhedron
    
using the faster binomial method

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#39389
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -1943,15 +1943,14 @@ cdef class CombinatorialPolyhedron(SageObject):
         """
         if self.is_simplex():
             return self.dim() + 1
-        else:
-            from sage.arith.misc import binomial
-            k = 1
-            while self.f_vector()[k+1] == binomial(self.n_vertices(), k + 1):
-                k += 1
-            return k
+        cdef int k = 2
+        f = self.f_vector()
+        while f[k] == self.n_vertices().binomial(k):
+            k += 1
+        return k - 1
 
     @cached_method
-    def is_neighborly(self, k=None):
+    def is_neighborly(self, k=None) -> bool:
         r"""
         Return whether the polyhedron is neighborly.
 
@@ -2000,7 +1999,7 @@ cdef class CombinatorialPolyhedron(SageObject):
         return all(self.f_vector()[i+1] == binomial(self.n_vertices(), i + 1)
                    for i in range(1, k))
 
-    def is_simplex(self):
+    def is_simplex(self) -> bool:
         r"""
         Return whether the polyhedron is a simplex.
 
@@ -2014,10 +2013,10 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: CombinatorialPolyhedron([[0,1],[0,2],[1,2]]).is_simplex()
             True
         """
-        return self.is_bounded() and (self.dim()+1 == self.n_vertices())
+        return self.is_bounded() and (self.dim() + 1 == self.n_vertices())
 
     @cached_method
-    def is_simplicial(self):
+    def is_simplicial(self) -> bool:
         r"""
         Test whether the polytope is simplicial.