Yes.
There are three "diamond shaped" rooms that appear in (normally) explorable areas of the map: D05 (near the Tayari beacon you mentioned), D06 (the Squidhenge), and D04 (the pod room). There may also be a fourth in inaccessible District 2. District 2 is a direct copy (in structure) of District 06... so there is a higher likelihood that its "Diamond Room" contains a Squidhenge.
So why do all Diamond Rooms indicate a "henge" structure in the VISR map? One explanation I have seen given more than once (I'm paraphrasing) is that the map representation of the Diamond Rooms in D04 and D05 was copied from D06. Others feel that a henge structure may appear in D04 and D05 under the "right conditions".
Given the current lack of morale we're seeing as discoveries in the Glyph and Henge direction have lulled (and my video teetering on the brink of being "Gothied") I think the former explanation is more publicly favored.
I doubt Bungie will cop to there being glitches/anomalies in their game even if there are; in which case, we'll have to figure it out on our own.
One glimmering hope in this direction is to get a sneak-peek of D02 from the work of the
Black Ops team, led by
VsH Tepec Fett. He remains confident that there may be a method to access District 02, albeit though somewhat "glitchy" methods.
