Name of irregular convex octahedron

Question

I wonder about the name of the following irregular convex octahedron:

• You can create it by taking a regular pentagon on the xy plane, and then duplicating one vertex, and changing the z coordinate of this two vertices, sending one vertex up and one vertex down by the same length.
• Or you can think of it as the Convex hull of this points

The final polyhedra will have 6 vertex, 12 edges, 8 faces and it will be convex. I hope there is a name for it since it has very specific symmetries.

Answer 1

It is an example of a biaugmented tetrahedron. Wolfram MathWorld calls it a boat. (These links show images of a topologically equivalent polyhedron with all equilateral triangles, but which is not convex; your octahedron is convex but consists of non-equilateral triangles. MathWorld includes a picture of a convex "boat" on the page Octahedron, but it doesn't have the same symmetry as your construction.)

It is one of only two convex polyhedra with 8 faces and 6 vertices (as you can see at Counting Polyhedra). Three possible Schlegel diagrams were given on Steven Dutch's Enumeration of Polyhedra page:

Its dual is this guy:

which can be called a pentagonal wedge.