code: def euler_characteristic_check(sphere, chi=2):
      r"""Checks the euler characteristic of a sphere
  
      If $f$ = number of faces, $e$ = number_of_edges and $v$ = number of
      vertices, the Euler formula says $f-e+v = 2$ for a mesh on a sphere. More
      generally, whether $f -e + v == \chi$ where $\chi$ is the Euler
      characteristic of the mesh.
  
      - Open chain (track) has $\chi=1$
      - Closed chain (loop) has $\chi=0$
      - Disk has $\chi=1$
      - Sphere has $\chi=2$
      - HemiSphere has $\chi=1$
  
      Parameters
      ----------
      sphere : Sphere
          A Sphere instance with vertices, edges and faces attributes.
      chi : int, optional
         The Euler characteristic of the mesh to be checked
  
      Returns
      -------
      check : bool
         True if the mesh has Euler characteristic $\chi$
  
      Examples
      --------
      >>> euler_characteristic_check(unit_octahedron)
      True
      >>> hemisphere = HemiSphere.from_sphere(unit_icosahedron)
      >>> euler_characteristic_check(hemisphere, chi=1)
      True
  
      """
      v = sphere.vertices.shape[0]
      e = sphere.edges.shape[0]
      f = sphere.faces.shape[0]
      return (f - e + v) == chi
  
imports: import numpy
  import warnings
  from scipy import optimize
  from dipy.core.geometry import cart2sphere, sphere2cart, vector_norm
  from dipy.core.onetime import auto_attr
  from dipy.reconst.recspeed import remove_similar_vertices
label_desc: Use image node_id 15 for calling a global function with example usage: euler_characteristic_check(sphere, chi) and returns: unknown