Acronym sheat
Name stellated heptagonal tiling,
hyperbolic order 7 heptagram tiling
Circumradius sqrt[(1-cos2(π/7))/(1-2 cos(π/7))] = 0.484510 i
Vertex figure [(7/2)7]
Dual o7/2o7x
related tesselations:
wikipedia   polytopewiki   nan ma

This hyperbolic star tiling can be obtained as a stellation of o3o7x. Every part of the tiling will be covered twice: by the convex central part and by the pointy ones.

The right picture, by courtesy of Nan Ma, dynamically shrinks the heptagrams, so that those can be spotted easier. – The left one on the other hand uses colorings instead. Even though, the centers of the heptagrams do belong to them also.

Like o3o7x this tiling allows for the according mod-wrap too, then being nothing but the "small stellated quart = sisqua". It thence has the same amount of faces, corresponding to choosing N=12 below.

Incidence matrix according to Dynkin symbol

x7/2o7o   (N → ∞)

.   . . | 2N |  7 |  7
x   . . |  2 | 7N |  2
x7/2o . |  7 |  7 | 2N

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