  import fealpy
import matplotlib.pyplot as plt

# Define nodes and cells for the mesh
nodes = [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1], [1, 1, 1]]
cells = [[0, 1, 2, 3], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]]

# Calculate number of nodes, edges, faces, and cells
num_nodes = len(nodes)
num_edges = len(cells) * 4
num_faces = len(cells) * 2
num_cells = len(cells)

# Calculate barycenter coordinates for each entity
barycenter_nodes = [sum(nodes[i]) / 3 for i in range(num_nodes)]
barycenter_edges = [sum(nodes[i] + nodes[j]) / 6 for i in range(num_edges) for j in range(i + 1, num_edges)]
barycenter_faces = [sum(nodes[i] + nodes[j] + nodes[k]) / 9 for i in range(num_faces) for j in range(i + 1, num_faces) for k in range(j + 1, num_faces)]
barycenter_cells = [sum(nodes[i] + nodes[j] + nodes[k] + nodes[l]) / 12 for i in range(num_cells) for j in range(i + 1, num_cells) for k in range(j + 1, num_cells) for l in range(k + 1, num_cells)]

# Calculate measure of each entity
measure_nodes = [sum(nodes[i]) for i in range(num_nodes)]
measure_edges = [sum(nodes[i] + nodes[j]) for i in range(num_edges) for j in range(i + 1, num_edges)]
measure_faces = [sum(nodes[i] + nodes[j] + nodes[k]) for i in range(num_faces) for j in range(i + 1, num_faces) for k in range(j + 1, num_faces)]
measure_cells = [sum(nodes[i] + nodes[j] + nodes[k] + nodes[l]) for i in range(num_cells) for j in range(i + 1, num_cells) for k in range(j + 1, num_cells) for l in range(k + 1, num_cells)]

# Calculate relationships between entities
relationships = []
for i in range(num_cells):
    for j in range(i + 1, num_cells):
        relationships.append([i, j])

# Identify boundary flags for each entity
boundary_flags = []
for i in range(num_nodes):
    if i in cells:
        boundary_flags.append(True)
    else:
        boundary_flags.append(False)
for i in range(num_edges):
    if i in cells:
        boundary_flags.append(True)
    else:
        boundary_flags.append(False)
for i in range(num_faces):
    if i in cells:
        boundary_flags.append(True)
    else:
        boundary_flags.append(False)
for i in range(num_cells):
    if i in cells:
        boundary_flags.append(True)
    else:
        boundary_flags.append(False)

# Identify indices of boundary nodes, edges, faces, and cells
boundary_nodes = [i for i in range(num_nodes) if boundary_flags[i]]
boundary_edges = [i for i in range(num_edges) if boundary_flags[i]]
boundary_faces = [i for i in range(num_faces) if boundary_flags[i]]
boundary_cells = [i for i in range(num_cells) if boundary_flags[i]]

# Plot the mesh using matplotlib
fig, ax = plt.subplots()
ax.scatter(nodes[:, 0], nodes[:, 1], nodes[:, 2], c=boundary_flags)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()