Quartz Twins
Quartz has many types of twins. Many are Contact Twins where two crystals are obviously joined together (as in Japan Law Twins). More subtle are the Penetration Twins which share the same axis and look like one crystal (Dauphiné and Brazil Law Twins). Penetration Twins result from Transformation. Transformation twinning occurs when a pre-existing crystal undergoes a change in pressure or temperature. During cooling, different parts of the Quartz become arranged in different symmetrical orientations. In Quartz Penetration Twins, the most obvious signs are the x-faces and s-faces.
My right-handed smoky quartz Dauphiné twin showing 2 triangular x-faces. The x-face in the second image also borders and is truncated by a diamond-shaped s-face. Similar to smoky quartz crystals from Graubünden, Switzerland and Morocco.
At first I thought this was a left-handed quartz Dauphiné twin showing 2 triangular x-faces. However the second x-face seems to border on a right-handed x-face on the adjoining side. Both of which also border a very small s-face on the corner with the cap, which you might just be able to make out. I have not found a diagram to match this.
This diagram has been adapted to show the extra x-face in grey. It may be either a rare complex compound twin or just a stray facet of no interest. You would need an expert to resolve this.
