In geometry, the elongated gyrobifastigium or gabled rhombohedron is a space-filling octahedron with 4 rectangles and 4 right-angled pentagonal faces.

It has all 3-valence vertices and its dual has all triangular faces, including the snub disphenoid as a deltahedron with all equilateral triangles.

The elongated gyrobifastigium is the cell of the isochoric tridecachoron, a polychoron constructed from the dual of the 13-5 step prism, which has a snub disphenoid vertex figure.

A topologically distinct elongated gyrobifastigium has square and equilateral triangle faces, seen as 2 triangular prisms augmented to a central cube.

The elongated gyrobifastigium must be based on a rectangular cuboid or rhombohedron to fill-space, while the angle of the roof is free, including allowing concave forms.