My interest is John Michell's Perpetual Choir theory: a Circle of ten Perpetual Choirs (CPC), including Glastonbury and Stonehenge, and centred on Whiteleaved Oak, near Ledbury. It's purpose?  "Celebrating the order of the heavens and guiding the ritual order of life on earth" (CITY OF REVELATION, John Michell, 1972).  An unending song, healing, harmonising and enchanting the land, some say, in tune with the changing seasons and the heavens.  John wrote (p.84) that the idea might not be "altogether fanciful", given certain (and supposedly significant) dimensions attached, these being 504 and 3168 furlongs.  For some - John Michell, Bonnie Gaunt et al - these numbers are "magnificent", the latter being, to John, "the perimeter of the temple", with 504 being the distance from centre to vertices.  The numbers are, it seems, those of sacred spaces, the dimensions of paradise..

Above are both John's original 1972 CITY OF REVELATION and his later DIMENSIONS OF PARADISE CPC diagrams, detailing 4 of 10 proposed CPC vertices.  And the basis for this CPC idea?  Well - at least partly - Plato, but mostly William Probert's 1823 (mis)translation/substitution in the relevant triad, from the equally iffy "third series" of Y MYVYRIAN ARCHAIOLOGY (Vol. 2, 1801, Iolo Morganwg, Owen Jones and Owen Pughe - abbr. Y Myvyr. below).  Neither translation nor source can be provenanced from any  legitimate sources. Probert writes:

"84 The three perpetual choirs of the Isle of Britain: the choir of Llan Illtyd Vawr, Glamorganshire; the Choir of Ambrosius in Ambresbury; and the choir of Glastonbury. In each of these three choirs there were 2,400 saints; that is, there were a hundred for every hour of the day and the night in rotation, perpetuating the praise and service of God without rest or intermission."   https://en.wikisource.org/wiki/Triads_of_Britain

Basic triad versions before this comprised just Bangor, *Glastonbury and Caer Caradoc, with others, I call Elaborate, giving some attempt to identify at least one of these - M/Bangor as Bangor-on-Dee - with various commonly ascribed terms (probably) identifying Glastonbury - *Ynys Avallach/Bangor Widrin etc. See https://perpetualchoirs.webador.co.uk/the-triad-background

So, here, where the first choir above would elsewhere commonly read just Bangor/Mangor (Iscoed/on-Dee), in Probert we see Llan Illtyd Vawr (Llantwit Major).  That's c/o Iolo, Y Myvyr.  Where the second choir would - again - commonly - just read Caer Caradoc, in the third series of Y Myvyr. we read Choir Ambrosius (Emrys) at Caer Caradoc.  This c/o  Iolo again, and/or Owen Pughe.  And, where, lastly, it should read this Choir Ambrosius at Caer Caradoc in Probert's "translation", possibly c/o Owen Pughe, again,  we actually read (in the above) the Choir of Ambrosius in Ambresbury.  Caer Caradoc is now (somehow) Ambresbury ..- and, to get from this Ambresbury to a Stonehenge substitution, we just need John Michell (with a little possible help from the Reverend Smithett, Mrs Robert Sewell and Elizabeth O Gordon).

So, Llantwit Major, Stonehenge and Glastonbury - John Michell's start threesome.  And, looking at a map (whils't on a trip, apparently), he noticed an angle of about 144 degrees between these 3 sites. This led to an epiphany of sorts: 144 degrees suggests decagon (comprising ten isosceles triangles angled 72-72-36) because each outer corner/vertex is 144 degrees (72 + 72), this being another "amazing" number*  John's triad "contribution"?  The substitution of Stonehenge for (the Choir of Ambrosius in) Ambresbury.  From this came the 144 degree angle of Llantwit Major with Stonehenge via Glastonbury.  And so also came Goring.  And so it began:  1972.

*https://www.amazon.co.uk/Beginnings-Sacred-Design-Bonnie-Gaunt/dp/093281378X 

Besides Michell's inventiveness regarding Stonehenge here, on top of the Probert mistranslation concern (which Probert knew of but deemed of no consequence), and the even more iffy provenance of his Y Myvyr. source, anyway,  there's another immediate problem: plane/flat geometry - that of decagons, for example - is meaningless applied (as Michell and others have done, and I boldly will) to curved surfaces over any great distance (40 miles + or so). To illustrate, draw a triangle on a piece of paper and then wrap a tennis ball in that piece of paper.  What happens to the triangle?

However - and despite all this - accepting (flat) Ordnance Survey maps as a base for enquiry, possibly significant things just seem to happen.  So my intention is to try to build a framework on which to hang Michell's (original) decagon/CPC idea - and see where it takes us, if anywhere.  Why?  Well, it's just a hobby of mine - and the subject has fascinated not just me but quite a few others: dowsers, musicians, spiritual healers ...

Quite arbitrarily, we start here: two moved stones, the Devil's Ring and Finger.

The Devil's Ring and Finger (SJ707378)  https://www.megalithic.co.uk/article.php?sid=4985   

Note: You can input OS coordinates here:  https://osmaps.ordnancesurvey.co.uk/   
Search for "Location" box, top left, and enter SJ707378). Press the magnifying glass . Then zoom in (top right).
For some possible background
https://thehistorydetective.org/2019/02/15/the-devils-ring-and-finger/

The earliest photo/record I've found so far dates to Wells Bladen W, 1912, North Staffordshire Field Club, Annual Report and Transactions 1911-1912. 

These stones are also known as the Whirl Stones.  They are by the Roman road Leominche and near the River Tern.  Roman (and other old) roads, rivers and river fords will be something of a feature.

"Holey" Hampnett 51 50, Phi (OS SP087151)    https://www.megalithic.co.uk/article.php?sid=6333494 

Secondly, we're at Hangman's, Hampnett. Another moved/abandoned stone.  Note the latitude: 51 50. Whereas 51 51 can denote pi, 51 50 can denote phi (Sq Rt 1.618 ... is 1.272 ... and tan 51 50 is 1.272 ...).  Phi is the Golden Mean/Divine Proportion.  Kepler called it a "precious gem" (with pi as "mass of gold").

There are 2  different stones at (Northleach) Hampnett. One - "Hangman's" - is set in the wall, and such stones are of a tradition (of sheep-rustling) going back hundreds of years. The other stone - "holey", I call it (because of the hole!) - is the unaccounted for one that you are asked to pick out here.  It actually looks noose-like (hence the confusion?).

Devil's Ring and Finger and "Holey" Hampnett have both been moved/abandoned at sites that can turn out to have a precise mathematical relationship: phi (again).  "Holey" Hampnett is near the Fosse Way and on an old Salt Road from Droitwich.  The nearby river is the River Leach.

Point St. John 3113' (OS SM719258)

https://getoutside.ordnancesurvey.co.uk/local/point-st-john-pembrokeshire-sir-benfro

This is our 3rd model "fix", along with the Devil's Ring and "Holey" Hampnett.

An estate map exists from 1811 (held at NLW - and my thanks!) that references Point St John: - A Map of Trelithin, Trevithan, and Pencarnan Estate, 1811  - "Thank you for your enquiry regarding Map 7574. Having examined the map I can confirm that St. John's Point is shown on the map."  And they kindly sent me the proof, above.

Point St. John first appears on OS in 1843 (1").  The latitude of the "fix" is precise: 51 53.  That's 3113' minutes of latitude*.  Why it changed from St. John's Point to Point St. John I (currently) give in.

*I note the rough Giza pyramids' latitude of 31.13(E).  Of course, you need to be using the Greenwich Meridian as base 0 degrees to get that value.

My "fixes" above  - the Devil's Ring,"Holey" Hampnett and Point St. John - are utterly arbitrary.  I found them starting (as John Michell did) with Stonehenge, Glastonbury, Llantwit, Whiteleaved Oak (centre) and Goring.  Establishing the connection between the Devil's Ring and "Holey" Hampnett, using John Michell's original 63 mile radius and a 126 degree angle, thus establishing a Raggedstone Hill (as it turned out) centre - just above John's Whiteleaved Oak candidate.  These, together with the phi relationship (and where one site establishing it actually sits on the phi latitude and the other progressed drops spot on the pi latitude) seemed as good a place as any to develop from in determining precise vertices for the decagon.  Given the Devil's Ring, Raggedstone Hill and "Holey" Hampnett threesome, you also get Point St. John (if you want).  I did not predicate any particular places at Glastonbury or Stonehenge to be vertices - I went where the model sent me.

Some incidental notes/OS grid peculiarity

All the "action" takes place between Lats. 51 and 53, and, with the some notable exceptions, like Point St. John, mainly on OS grid blocks SJ, SN, S0, SS and ST. SH completes the rectangle:

(SH) SJ
SN SO
SS ST

Can you find a "John" there and saint(s)?  I note the base grid behind this is STHN.  This particular OS grid nomenclature is less than 100 years old.

Raggedstone Hill 52.025 (OS SO761364)                                  

Raggedstone Hill, Malverns, just by Whiteleaved Oak (and across the road from the Midsummer Hill fort, Dyn Mawr).  This will be our model centre.  Avoid its shadow:  https://en.wikipedia.org/wiki/Raggedstone_Hill

To begin to build the framework of our CPC model, we join the Devil's Ring and Finger (Whirl Stones) to here, join here to Hangman's at Hampnett (51 50) and also join here to Point St. John (mirror 3113').
The distance from Devil's Ring to here will be 63 miles exactly (it's to be our radius r/John Michell's 504 furlongs) and from here to Hangman's is phi-squared r, 24.06 ... miles, again exactly (+ or - 100 metres or so). The diameter, of course, is 63 X 2 = 126 miles - and the angle between Devil's Ring and Hampnett Hangman's is 126 degrees (90 + 36) exactly.  This 36 degrees is the maths of decagons (360/10).  The model's start radius is angled exactly 3 degrees off OS "up" (also implying 33 c/o decagonal 36 - 3, and 57 c/o 90 - 33). It's all just a tad masonic, really, 3 degrees and 33 degrees?

The Latitude of Raggedstone?  Mirror 52.025.  Continue from Devil's Ring and Finger through here on to Elmore Back (and the "pi" Latitude 51 51) and this delivers the centre for an octagon at Elmore Back, by the River Severn .... if you want one (SO772161). The octagon would have a radius of 50.4 miles, diameter 100.8.  Circumference x 22/7 (but not real pi!) = 316.8. The decagon would have a radius of 504 furlongs and a 22/7 circumference of 3168 furlongs (again, John Michell's numbers from the start).

Using 22/7 for pi?  Well it's not-quite-right or simply just-plain-wrong maths.  But it turns out "pretty" results (like 3168 - Gematria Lord Jesus Christ).

Pen du Goedydd (Llwynywormwood)   (OS SN748311)
https://getoutside.ordnancesurvey.co.uk/local/allt-pendugoedydd-carmarthenshire-sir-gaerfyrddin

We can now draw a circle radius 63 miles centred on Raggedstone Hill. The 22/7 circumference is 396 miles. This circle cuts our line from Raggedstone to Point St John here (near the Afon Ydu): the middle of nowhere ... and this is our first decagon vertex.  Note Llwynywormwood Farm just to the east).  I believe King Charles owns it.
 
There is a standing stone to the south at Cilgwyn on or just by our circumference @ SN749301. There's a plaque on it saying it was moved to its present site in 1825 from Beili-Glas. There's a curiosity here in that 1.825 degrees of Latitude = 126 miles, and, if we develop our start radius - of Devil's Ring to Raggedstone Hill - down through Elmore Back and on, to meet this circle (thus creating a model axis), we will have a model diameter of 126 miles, our 63 mile radius X 2.   And we will be at mirror Lat. 51.115, near White Sheet Hill and castle, (ST815352), near Mere Down and Great Bottom, and equidistant from Stonehenge and Glastonbury.  A nearby nicety to this site is "The Convent", Stourhead, by the bottom of a vertical bisection of the CPC - http://www.alfredstower.info/Convent.aspx

396, our decagonal model's circumference - c/o the 126 mile diameter X 22/7 - is 1/20th of a stylised Earth diameter of 7920, noting (octagonal) 316.8 is 4/5ths of this 396.

The Roman Via Julia Montana (A40) is across the River Towy.  The nearest river is the Afon Ydw.

Enderby, slightly NNW of Aldeby St. John's ruin (SK549002) https://www.flickr.com/photos/stefancabaniuk/4210701425

We are now in a position to identify all the other corners/vertices of our decagon.  One is at Leicester, just off the Fosse Way at Fosse Park.  A nearby road is "St Johns" and note also the nearby Johnstone Spinney. King Llyr is reputedly buried under the River Soar thereabouts. There's a nearby ruined St. John's church (SP553 990):   ancientmonuments.uk 

"All that remains of the church of S. John at Aldeby to-day is an oblong mound, 72 ft. by 30 ft., standing in field No. 195, close to the river bank; there is a modern wooden cross on the east end of the mound, and a service is held there annually by the vicars of Enderby, on the Sunday nearest to S. John's day. It was duly held in 1929 on the afternoon of 23 June."  www.le.ac.uk

So we are talking John the Baptist (24th June birthday), Aldeby and, possibly, Llyr. Now a son of Llyr was Bran the Blessed, associated with the alder tree. Robert Graves (The Greek Myths) calls him the Alder-god. John the Baptist and Bran have being beheaded in common. 

Llantwit Major/Llaniltud Fawr (or Nash Manor)     (SS973726)

https://osmaps.ordnancesurvey.co.uk/51.44305,-3.47910,14/pin

(The "Caer Worgan site" detail above is from an interactive here https://maps.nls.uk/view/10234265            Click on the "C" bottom middlish twice and look to the left).

These are near one of  Michell's "Eureka" start vertices, Lantwit Major/Llaniltud Fawr. But note that, by DIMENSIONS OF PARADISE, John had moved north of this city site slightly (see the diagrams up top). To be precise with Michell's terminology here, as well, he tells us that Llantwit Major is variously at, by, or near his vertex (depending on which book of his you read). This vertex actually opposes Aldeby St. John's across our (developing) decagon.  Above are the Caer Worgan detail and an old OS extract of Nash Manor, with a slightly more recent document below it.  Both carry "monastery" and are thereabouts.  Here's the 1885 OS map: https://maps.nls.uk/view/102342652 .  Click on the map and it will enlarge to show "monastery" at Nash.

OS, however, no longer carries this identification.  Genuki however carries: "Nash (121); Monastery (Remains of); Nash Manor" under section Names, Geographical: https://www.genuki.org.uk/big/wal/GLA/Llysworney

For me, the vertex of the decagon location is much more this Nash Manor area, most particularly Moorshead farm, than Llantwit. There is a Roman road hereabouts (from Llantwit to Cowbridge), the B4270.  I note nearby Caermead (SS959700) has a Roman Villa associated by some with St. Eurgain, the legendary Virgin Foundress of Glamorgan, and at Lat.51.4192, the parthenos (virgin) latitude 51.4-51.5, aka 360/7, also the Avebury latitude.  Llantwit itself, or at least nearby Caer Worgan (a site adjoining Caermead), was cited as a Perpetual Choir site by Edward Williams (Iolo Morganwg) in Y MYVYRIAN ARCHAIOLOGY.  The Llantwit area religious foundation(s) was/were - variously - the doing of the aforesaid Eurgain, a Roman Emperor Theodosius and/or St. Illtyd/Iltutus: see
 https://en.wikipedia.org/wiki/Illtud and
https://books.google.co.uk/books?id=EnEBAAAAQAAJ&pg=PA86&lpg=PA86&dq=caer+worgan+history&source=bl&ots=qhvW3_fgOI&sig=ACfU3U2XLwXpGsGJCpyQNmxif8n3SRiY9g&hl=en&sa=X&ved=2ahUKEwiD3__jrNfjAhXGi1wKHayXC4wQ6AEwBHoECAgQAQ#v=onepage&q=caer%20worgan%20history&f=false

Or - there again - partly an Iolo fabrication: https://en.wikipedia.org/wiki/C%C3%B4r_Tewdws

But there was a famous college there from C6th AD known as Bangor Illtyd and there is mention of a monastery at Llantwit here (under "St. Illtud's School, Bangor Illtyd"):   https://en.wikipedia.org/wiki/St_Illtyd%27s_Church,_Llantwit_Major

Glastonbury/Ynys Widrin   (ST499385)  (and the vesica at Chalice Well)

Another of Michell's three "Eureka" vertices is here: osmaps.ordnancesurvey.co.uk

My site comes out near the southern end of Magdalene Street, by the Abbey grounds, and near St. Mary's church. To the north are St John's Square and (Baptist) church. Across the road is St. John's Chapel (aka Dunstan's), on - or very near to - the site of the original church on the site (pre-Abbey).  A detail from its sitemap:
https://research.reading.ac.uk/glastonburyabbeyarchaeology/digital/the-cloister-c-1150s/monastic-life/

"The Roman Way" is nearby (I think it's a housing estate).  The nearest river is the River Brue.  I read of evidence of a monastery at Beckery https://www.bbc.co.uk/news/uk-england-somerset-38187299

Old Stratford, Watling Street/stream off Dogsmouth Brook (River Great Ouse)  (SP774417) 

Map from: https://www.getthedata.com/postcode/MK19-6AN

This is the vertex opposite the "Llwynywormwood" area one.  There a strong associations with "St. John of Jerusalem": http://www.mkheritage.co.uk/os/doc/his/hos.html and   https://www.british-history.ac.uk/vch/bucks/vol4/pp476-482
​
"In this part of Stony Stratford, called Bridge End in the 16th century from its proximity to the bridge spanning the Ouse, (fn. 10) stood the leper hospital of St. John the Baptist without Stony Stratford. It was described in the 14th century as situated near 'le Shrob' and the causeway leading to the bridge. (fn. 11) It was in existence probably before about 1240, in which year William de Paveli bequeathed 12d. 'infirmis de Straford,' (fn. 12) and certainly before 1257. (fn. 13) In 1329, however, the master and brethren were found to be 'without the means of living unless others come to their aid,' (fn. 14) and in 1352 their chapel was 'for the most part in ruins.'" (fn. 15)."

The vertex is by the A5/Watling roundabout and "Shrobb".  The leper hospital was probably slightly south-west by the Watling and the Great Ouse.  This is very close to where Richard, Duke of Gloucester, intercepted the young King Edward V. 

Goring-on-Thames et al  (SU611812)  Old OS detail "The Temple" and Map an extract from http://www.visitgoringandstreatley.co.uk/local-walks--cycling.html

There's Elvendon Priory at SU623813 but our "fix" is the Battle Plantation, Battle road, (noting Michell's "temple" site is at nearby Cleeve):  
https://getoutside.ordnancesurvey.co.uk/local/battle-plantation-south-oxfordshire   Click + a couple of times to see the plantation, the road and nearby Elvedon Priory cottages.  Apparently, there's no evidence there ever was an actual priory there.

John Michell and Robin Heath visited Goring whilst preparing THE MEASURE OF ALBION (aka THE LOST SCIENCE OF MEASURING THE EARTH). They came across "The Temple".  Seemed to confirm the 4th site.  Unfortunately, a C19th AD oil painting exists of the site as virgin greenfield (before a London merchant built his "The Temple" on it).   The nearby Temple boathouse (once owned by the Who's Pete Townsend)  still exists. The area has been suggested as the site of an Arthurian battle:

"The Strife of Camlann in which Arthur and Medraut perished".

"Over the years, it has been variously identified as being at Queen or West Camel on the River Cam, Somerset; at Slaughter Bridge on the River Camel in Cornwall; at Camelon, Stirlingshire or Salisbury Plain, Wiltshire. Recent suggestions indicate Goring Gap on the Thames at the Berkshire/Oxfordshire border or Cadnam in the New Forest."  http://www.earlybritishkingdoms.com/arthur/kabattles.html

We are close to the River Thames crossing and the Icknield Way.

The back of beyond:   (SN911916).  

There's a place in the absolute back of beyond, to the left of Llawryglyn and Gwernafon. It's below the hillfort at Cefn-y-Cloddiau to the south and Wern Screwd to the west. A Roman Road is posited to run Caersws-Trefelgwys-Staylittle-Dylife possibly runs through or near the site.  A nearby feature is "Stepping Stones".  The nearby stream is Nant Ysgiliwch.

The remaining vertices are all out in the sticks. too. One is by Godstone and Dod's Leigh, on the banks of the River Blithe (SK024343). Another is a "toot" - Dandyford - that used to be an island on Tetchhill Moor when it was (once) a mere (SJ399311).  And, lastly, there's some stones dumped near Amesbury.  Oh, yes: Stonehenge....  My derived grid reference for this is SU124417.  This is not the monument's centre.  The nearby river is the Avon.  Source: https://en.wikipedia.org/wiki/Stonehenge

The Circle of the Perpetual Choirs of Britain: