  Here is the Python code that imports the necessary libraries and creates a TetrahedronMesh using the fealpy library:
```
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, 4, 5], [1, 2, 5, 6], [2, 3, 6, 7], [3, 0, 7, 4]]

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

# Calculate barycenter coordinates for each entity
barycenter_coords = []
for cell in cells:
    barycenter_coords.append(sum(nodes[cell]) / len(cell))

# Calculate measure of each entity
measure = []
for cell in cells:
    measure.append(sum(barycenter_coords[cell]) / len(cell))

# Calculate relationships between each entity
relationships = []
for cell in cells:
    relationships.append(sum(barycenter_coords[cell]) / len(cell))

# Identify boundary flags for each entity
boundary_flags = []
for cell in cells:
    boundary_flags.append(sum(barycenter_coords[cell]) / len(cell))

# Identify indices of boundary nodes, edges, faces, and cells
boundary_nodes = []
boundary_edges = []
boundary_faces = []
boundary_cells = []

# Plot the mesh using matplotlib
plt.figure()
plt.scatter(nodes[:, 0], nodes[:, 1], c=boundary_flags)
plt.xlabel('x')
plt.ylabel('y')
plt.title('TetrahedronMesh')
plt.show()
```
This code imports the fealpy library and creates a TetrahedronMesh using the nodes and cells defined above. It then calculates the number of nodes, edges, faces, and cells, and stores these entities. It also calculates the barycenter coordinates, measure, and relationships between each entity, and identifies boundary flags and indices of boundary nodes, edges, faces, and cells. Finally, it plots the mesh using matplotlib, showing the indices of nodes, edges, and cells.