The pentagonal wegde is one of the seven topologically distinct convex hexahedra. Like the cube, it contains 8 vertices, 12 edges, and 6 faces, but its faces consist of 2 triangles, 2 quadrilaterals, and 2 pentagons. As illustrated above, it can be constructed by truncating two of the corners of a tetrahedron.
A symmetrical pentagonal wedge can be built with two regular pentagons and two equilateral triangles, leaving a single edge (the longest side of the two remaining trapezoidal
faces) of different length. In particular, the long edge is a factor of the golden
ratio 
times the other edge lengths.
The trapezoids of the symmetrical pentagonal wedge have angles 
and 
, as illustrated in the net above.
This almost-unit pentagonal wedge is implemented in the Wolfram Language as PolyhedronData["PentagonalWedge"].
For short side lengths 
,
the symmetrical pentagonal wedge has a circumsphere
of radius
 |
(1)
|
and volume
 |
(2)
|
The dihedral angle between the two pentagons is
 |  |  |
(3)
|
 |  |  |
(4)
|
