The gyrated triangular prismatic honeycomb or parasquare fastigial cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triangular prisms.
It is vertex-uniform with 12 triangular prisms per vertex.

It can be seen as parallel planes of square tiling with alternating offsets caused by layers of paired triangular prisms.
 The prisms in each layer are rotated by a right angle to those in the next layer.

It is one of 28 convex uniform honeycombs.

Pairs of triangular prisms can be combined to create gyrobifastigium cells.
The resulting honeycomb is closely related but not equivalent: it has the same vertices and edges, but different two-dimensional faces and three-dimensional cells.
The gyrated triangular prismatic honeycomb or parasquare fastigial cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triangular prisms. It is vertex-uniform with 12 triangular prisms per vertex.
It can be seen as parallel planes of square tiling with alternating offsets caused by layers of paired triangular prisms.  The prisms in each layer are rotated by a right angle to those in the next layer.
It is one of 28 convex uniform honeycombs.
Pairs of triangular prisms can be combined to create gyrobifastigium cells. The resulting honeycomb is closely related but not equivalent: it has the same vertices and edges, but different two-dimensional faces and three-dimensional cells.
Triangular prismatic honeycomb