⭳

The base face {(hhH)²} has corner angles of h = 108° and H = 144°. Note that h is the same corner angle as the pentagon, thence that non-regular hexagon reuses 4 out of 5 vertices of such a virtually inscribed pentagon. The 2 other here existing pentagons together with this virtual one then would outline an inscribed teddi.

Alternatively it can be viewed as half of bilbiro. In fact, its pointwise mirroring with respect to the center of the hexagon would result in the latter.

Incidence matrix

2 * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0	[3,5,H]
* 2 * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 0	[3,5,h]
* * 2 * * * | 0 1 0 0 0 1 1 0 0 0 | 1 0 1 0 1 0	[3,4,h]
* * * 1 * * | 0 0 0 0 2 0 0 1 0 0 | 0 2 0 1 0 0	[3,52]
* * * * 2 * | 0 0 1 0 0 0 1 0 1 1 | 0 1 1 0 1 1	[3,4,3,5]
* * * * * 1 | 0 0 0 0 0 0 0 1 0 2 | 0 2 0 0 0 1	[3,52]
------------+---------------------+------------
1 1 0 0 0 0 | 2 * * * * * * * * * | 1 1 0 0 0 0
1 0 1 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0 0
1 0 0 0 1 0 | * * 2 * * * * * * * | 0 1 1 0 0 0
0 2 0 0 0 0 | * * * 1 * * * * * * | 1 0 0 1 0 0
0 1 0 1 0 0 | * * * * 2 * * * * * | 0 1 0 1 0 0
0 0 2 0 0 0 | * * * * * 1 * * * * | 1 0 0 0 1 0
0 0 1 0 1 0 | * * * * * * 2 * * * | 0 0 1 0 1 0
0 0 0 1 0 1 | * * * * * * * 1 * * | 0 2 0 0 0 0
0 0 0 0 2 0 | * * * * * * * * 1 * | 0 0 0 0 1 1
0 0 0 0 1 1 | * * * * * * * * * 2 | 0 1 0 0 0 1
------------+---------------------+------------
2 2 2 0 0 0 | 2 2 0 1 0 1 0 0 0 0 | 1 * * * * *	{(hhH)2}
1 1 0 1 1 1 | 1 0 1 0 1 0 0 1 0 1 | * 2 * * * *	{5}
1 0 1 0 1 0 | 0 1 1 0 0 0 1 0 0 0 | * * 2 * * *	{3}
0 2 0 1 0 0 | 0 0 0 1 2 0 0 0 0 0 | * * * 1 * *	{3}
0 0 2 0 2 0 | 0 0 0 0 0 1 2 0 1 0 | * * * * 1 *	{4}
0 0 0 0 2 1 | 0 0 0 0 0 0 0 0 1 2 | * * * * * 1	{3}