Acronym hihexat Name hyperbolic order 6 hexagonal tiling ` ©   ` Circumradius 1/sqrt(-8) = 0.353553 i Vertex figure [66] Dual (selfdual) Confer more general: xPoPo   general polytopal classes: regular   noble polytopes Externallinks
` ©    ©`

There exists a regular modwrap of this tiling, obtained by identifying every 3rd vertex on each hole. Then it allows a representation as infinite regular skew polyhedron, which happens to be a facial subset of the bitruncated tetrahedral-octahedral honeycomb.

Incidence matrix according to Dynkin symbol

```x6o6o   (N → ∞)

. . . | N |  6 | 6
------+---+----+--
x . . | 2 | 3N | 2
------+---+----+--
x6o . | 6 |  6 | N
```

```s4o6o   (N → ∞)

demi( . . . ) | N |  6 | 6
--------------+---+----+--
s4o .   | 2 | 3N | 2
--------------+---+----+--
sefa( s4o6o ) | 6 |  6 | N

starting figure: x4o6o
```

```o3o4s4*a   (N → ∞)

demi( . . .    ) | 2N |  3  3 |  6
-----------------+----+-------+---
o   s4*a   |  2 | 3N  * |  2
. o4s      |  2 |  * 3N |  2
-----------------+----+-------+---
sefa( o3o4s4*a ) |  6 |  3  3 | 2N

starting figure: o3o4x4*a
```

```x3xØo3oØ*a

. . . .    | 2N |  3  3 |  6
-----------+----+-------+---
x . . .    |  2 | 3N  * |  2
. x . .    |  2 |  * 3N |  2
-----------+----+-------+---
x3x . .    |  6 |  3  3 | 2N
```