Carnedd Llywelyn sits at the centre of the long north-east to south-west spine of the Carneddau range, with Carnedd Dafydd to the south-west and Foel Grach to the north. A subsidiary ridge runs north-west to Yr Elen. The summit itself is a flat, boulder-strewn plateau, not a peak in the dramatic sense - more like the broken crown of an enormous ancient massif worn flat by ice. In winter the plateau holds snow in volumes rare elsewhere in Britain, and old snow patches survive in the southern gullies into July most years, sometimes later. The highest lake in Wales, Llyn Llyffant, sits in the lee of the summit, a pool of meltwater catching the slow drainage of those snowfields. The cliffs below the main ridges - Ysgolion Duon, "the Black Ladders," and Craig yr Ysfa - are among the most respected rock climbing crags in Snowdonia.

The story most often told is the obvious one: that Carnedd Llywelyn and the neighbouring Carnedd Dafydd are named for Llywelyn ap Gruffudd and his brother Dafydd ap Gruffudd, the last two princes of independent Wales. Both died at Edward's hands within months of each other in 1282-1283. An alternative tradition reaches further back, to Llywelyn the Great and his son Dafydd ap Llywelyn, the dynasty's earlier peak. Welsh writers and the Snowdonia National Park Authority prefer the spelling Llywelyn; the Ordnance Survey, settled into nineteenth-century habit, prints Llewelyn. The first recorded poem about the mountain is older than the dispute - Rhys Goch Eryri composed his "Carnedd Llywelyn" around 1400, when memory of the conquest was still close enough to mourn.

There are four classic ways up. From Gerlan above Bethesda the path follows the Afon Llafar deep into the cwm before climbing to the summit of Yr Elen and traversing the short connecting ridge. From Helyg on the A5 a track leads to Ffynnon Llugwy reservoir before the long climb up beside Craig yr Ysfa. The third option is the full ridge walk - Pen yr Ole Wen or Foel-fras to the summit - one of the great traverses in Wales. Most years the route is on grass and boulders. In a hard winter the plateau is closer to the Cairngorms than to anything south of Glasgow: knee-deep drifts, whiteout, and the constant risk of stepping off a cornice you cannot see.

On the night of 14 March 1950, several RAF Avro Lincoln bombers from No. 230 Operational Conversion Unit took off from RAF Scampton on a cross-country exercise. Weather closed in at home. A controller at RAF Barton Hall diverted three of the Lincolns to RAF Valley on Anglesey. At 2:55 a.m. on 15 March, the crew of RF511 lost contact. Five minutes later the other two aircraft landed safely. RF511 was found at 5:20 a.m. on Carnedd Llywelyn, wrecked across the plateau with all six crew dead. The Court of Inquiry concluded the pilot had misheard a radio instruction - "turn 180 degrees" became "turn 80 degrees," and a controlled flight into the highest ground in Gwynedd followed. The wreckage is still there. In 2002 a memorial plaque was placed at the crash site. Walkers crossing the summit in clear weather sometimes pause at a scatter of corroded aluminium and wonder what it is.

The Aetherius Society, a UFO religion founded by George King in the 1950s, lists Carnedd Llywelyn as one of nineteen holy mountains worldwide. The classification is unusual but the impulse is not. The summit plateau looks out over almost the whole of Snowdonia: Tryfan's spine to the south-west, the Glyderau's chaos beyond it, the Conwy's silver thread running north-east toward Llandudno, and on a clear day the Isle of Man rising from the Irish Sea. The high ground is mostly silent. The wind on the plateau in May still has winter in it. Llywelyn's cairn has been here for seven hundred years; the snow patches in the southern gullies are older than him by ten thousand.