class_docstr: Space of parameterized discrete surfaces.
  
  Each surface is sampled with fixed `n_vertices` vertices and `n_faces`
  faces in :math:`\mathbb{R}^3`.
  
  Each individual surface is represented by a 2d-array of shape
  `[n_vertices, 3]`. This space corresponds to the space of immersions
  defined below, i.e. the
  space of smooth functions from a template to manifold :math:`M`
  into :math:`\mathbb{R}^3`, with non-vanishing Jacobian.
  
  .. math::
      Imm(M,\mathbb{R}^3)=\{ f \in C^{\infty}(M, \mathbb{R}^3)
      \|Df(x)\|\neq 0 \forall x \in M \}.
  
  Parameters
  ----------
  faces : integer array-like, shape=[n_faces, 3]
      Triangulation of the surface.
      Each face is given by 3 indices that indicate its vertices.
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docstr: Extract 3D vertices coordinates corresponding to each face.
  
  Parameters
  ----------
  point : array-like, shape=[..., n_vertices, 3]
      Surface, as the 3D coordinates of the vertices of its triangulation.
  
  Returns
  -------
  vertices : tuple of vertex_0, vertex_1, vertex_2 where:
      vertex_i : array-like, shape=[..., n_faces, 3]
          3D coordinates of the ith vertex of that face.
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code: def _vertices(self, point):
      """Extract 3D vertices coordinates corresponding to each face.
  
      Parameters
      ----------
      point : array-like, shape=[..., n_vertices, 3]
          Surface, as the 3D coordinates of the vertices of its triangulation.
  
      Returns
      -------
      vertices : tuple of vertex_0, vertex_1, vertex_2 where:
          vertex_i : array-like, shape=[..., n_faces, 3]
              3D coordinates of the ith vertex of that face.
      """
      vertex = []
      for i in range(3):
          if point.ndim == 2:
              vertex_i = [point[index, :] for index in self.faces[:, i]]
          if point.ndim == 3:
              vertex_i = [
                  point[:, index, :] for index in self.faces[:, i]
              ]
          vertex.append(gs.stack(vertex_i, axis=-2))
      vertex_0, vertex_1, vertex_2 = vertex
  
      if point.ndim == 3 and vertex_0.ndim == 2:
          vertex_0 = gs.expand_dims(vertex_0, axis=0)
          vertex_1 = gs.expand_dims(vertex_1, axis=0)
          vertex_2 = gs.expand_dims(vertex_2, axis=0)
      return vertex_0, vertex_1, vertex_2
  
imports: import math
  import geomstats.backend
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.numerics.optimizers import ScipyMinimize
label_desc: Use image node_id 8 for calling the DiscreteSurfaces obj's underlying member method code with example usage: obj._vertices(point) and returns: vertex_0,  vertex_1,  vertex_2