What are faces of two triangles by planar_face_traversal?

Suppose we have two triangles, one have vertexes 0, 1, 2, the other have vertexes 3, 4, 5, then we use planar_face_traversal to traversal it, we will get 4 faces:
New face: 0 1 2
New face: 1 0 2
New face: 3 4 5
New face: 4 3 5
But I think we should only have three faces, we only have three regions in fact.
Anybody can explain the result?
Here is the code (https://godbolt.org/z/eKKffh1Mx):
```cpp
#include
#include
#include
#include
#include
#include
#include

#include
#include

using namespace boost;

// Some planar face traversal visitors that will
// print the vertices and edges on the faces

struct output_visitor : public planar_face_traversal_visitor
{
void begin_face() { std::cout << "New face: "; }
void end_face() { std::cout << std::endl; }
};

struct vertex_output_visitor : public output_visitor
{
template < typename Vertex > void next_vertex(Vertex v)
{
std::cout << v << " ";
}
};

struct edge_output_visitor : public output_visitor
{
template < typename Edge > void next_edge(Edge e) { std::cout << e << " "; }
};

int main(int argc, char** argv)
{

typedef adjacency_list< vecS, vecS, undirectedS,
property< vertex_index_t, int >, property< edge_index_t, int > >
graph;

// Create a graph - this is a biconnected, 3 x 3 grid.
// It should have four small (four vertex/four edge) faces and
// one large face that contains all but the interior vertex
graph g(6);

add_edge(0, 1, g);
add_edge(1, 2, g);
add_edge(2, 0, g);

add_edge(3, 4, g);
add_edge(4, 5, g);
add_edge(5, 3, g);

// Initialize the interior edge index
property_map< graph, edge_index_t >::type e_index = get(edge_index, g);
graph_traits< graph >::edges_size_type edge_count = 0;
graph_traits< graph >::edge_iterator ei, ei_end;
for (auto [ei, ei_end] = edges(g); ei != ei_end; ++ei)
put(e_index, *ei, edge_count++);

// Test for planarity - we know it is planar, we just want to
// compute the planar embedding as a side-effect
typedef std::vector< graph_traits< graph >::edge_descriptor > vec_t;
std::vector< vec_t > embedding(num_vertices(g));
if (boyer_myrvold_planarity_test(boyer_myrvold_params::graph = g,
boyer_myrvold_params::embedding = &embedding[0]))
std::cout << "Input graph is planar" << std::endl;
else
std::cout << "Input graph is not planar" << std::endl;

std::cout << std::endl << "Vertices on the faces: " << std::endl;
vertex_output_visitor v_vis;
planar_face_traversal(g, &embedding[0], v_vis);

std::cout << std::endl << "Edges on the faces: " << std::endl;
edge_output_visitor e_vis;
planar_face_traversal(g, &embedding[0], e_vis);

return 0;
}
```