<｜begin▁of▁sentence｜>### Instruction:
Imagine you're examining the remnants of a shipwreck, which for analysis's sake, can be seen as an intricate network of interconnected chambers and pathways. Your task is to map this structure in a way that reveals its complex connections, akin to the Tutte graph, a celebrated curiosity amongst mathematical structures. This web of chambers, akin to nodes, consists of 46 distinct compartments, all linked by 69 paths, resembling edges, forming a network that hints at the structure of a 3D polyhedron - each junction perfectly entwined with three passageways, much like a cubic lattice.

As this networked map is being crafted, you're curious to determine if there's a singular route that could take you on a tour through each chamber without retracing your steps - a path akin to what mathematicians call a Hamiltonian cycle. The Tutte graph, however, is notorious for defying such an existence, standing as a testament against an old assumption known as Tait's conjecture, which presumed every such three-valent (three connections per node) graph would possess such a cycle. 

Using NetworkX, a Python library tailored for the visualization and analysis of complex networks, you'd be able to digitally reconstruct the graph that mimics this shipwreck's compartment layout. While doing so, can you advise on the process of generating this non-Hamiltonian Tutte graph and creating a visual representation using NetworkX tools? If the layout is stored in a Graph Modelling Language file, please make sure to reference the file as "tutte_graph.gml".
### Response:
import networkx as nx

# Create the Tutte graph
G = nx.tutte_graph()

# Draw the graph
import matplotlib.pyplot as plt
nx.draw(G, with_labels=True)
plt.show()
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