The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals.
A tetragonal antiwedge can be constructed starting from two noncongruent quadrilaterals that share an edge (the "hinge"), adding edges between vertices to form two triangles whose sides are adjacent to the hinge, and then choosing the diagonal of the nonplanar quadrilateral opposite the hinge to give a convex solid.
The tetragonal antiwedge has the least possible symmetry of all convex hexahedra and is the only chiral convex hexahedron.
The canonical tetragonal antiwedge with midsphere centered at the origin, illustrated above, is implemented in the Wolfram Language as PolyhedronData["TetragonalAntiwedge"]. If the midsphere has unit length, the volume of the canonical tetragonal antiwedge is
 |  |  |
(1)
|
 |  |  |
(2)
|
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(3)
|
where 
is the golden ratio, which is a nice pi
approximation (cf. Pegg 2018).
The tetragonal antiwedge is self-dual, as illustrated above.
The skeleton of the tetragonal antiwedge is the tetragonal antiwedge graph (which is isomorphic to the 6-path
complement graph 
).
