Zigzag duocomb

Zigzag duocomb
Rank	3
Dimension	4
Type	Regular
Notation
Schläfli symbol	$\{4,4\}\#\{4\}$
Elements
Faces	MN  squares
Edges	2MN
Vertices	MN
Vertex figure	Skew square
Petrie polygons	N  Square helices
Related polytopes
Halving	Blended square tiling
Abstract & topological properties
Flag count	8MN
Schläfli type	{4,4}
Orientable	Yes
Genus	0
Properties
Convex	No
Dimension vector	(2,2,3)

The zigzag duocomb is a regular skew apeirohedron in 4-dimensional Euclidean space. It can be constructed as the comb product of two zigzags or as a blend of the square tiling with a square.

Vertex coordinates

The vertex coordinates of a zigzag duocomb with unit edge length can be given as:

• $({\sqrt {2}}i+m,{\sqrt {2}}j+n,m,n)$,

where $i,j\in \mathbb {Z}$ and $m,n\in \left\{0,{\sqrt {2}}/2\right\}$.