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Added a solid polyhedral portion of the unbounded polyhedron.
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Joseph O'Rourke
Joseph O'Rourke
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Not an answer; just an illustration.

I doubt this helps, but here is an indication of what the polyhedron would look like in $\mathbb{R}^3$:

          ![PolytopeMink][1]
The origin is green, $\{A_1, A_2, A_3\}$ are the three corners of the triangle, and the ribs of $\mathrm{cone}(e_1,e_2,e_3)$ are depicted at each vertex. One then has to imagine extending the ribs to $\infty$ and taking the convex hull. Here is a portion of that hull:
          ![PolytopeMinkSolid][2]

Not an answer; just an illustration.

I doubt this helps, but here is an indication of what the polyhedron would look like in $\mathbb{R}^3$:

          ![PolytopeMink][1]
The origin is green, $\{A_1, A_2, A_3\}$ are the three corners of the triangle, and the ribs of $\mathrm{cone}(e_1,e_2,e_3)$ are depicted at each vertex. One then has to imagine extending the ribs to $\infty$ and taking the convex hull.

Not an answer; just an illustration.

I doubt this helps, but here is an indication of what the polyhedron would look like in $\mathbb{R}^3$:

          ![PolytopeMink][1]
The origin is green, $\{A_1, A_2, A_3\}$ are the three corners of the triangle, and the ribs of $\mathrm{cone}(e_1,e_2,e_3)$ are depicted at each vertex. One then has to imagine extending the ribs to $\infty$ and taking the convex hull. Here is a portion of that hull:
          ![PolytopeMinkSolid][2]
Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

Not an answer; just an illustration.

I doubt this helps, but here is an indication of what the polyhedron would look like in $\mathbb{R}^3$:

          ![PolytopeMink][1]
The origin is green, $\{A_1, A_2, A_3\}$ are the three corners of the triangle, and the ribs of $\mathrm{cone}(e_1,e_2,e_3)$ are depicted at each vertex. One then has to imagine extending the ribs to $\infty$ and taking the convex hull.