The question that started this wasn't about clocks. It was about what happens when you remove every cultural assumption from timekeeping and ask: what's left?

This still measures the time of day in seconds since midnight. It still encodes the number of seconds into the common base 60 system of hours, minutes, and seconds. It still encodes the base 60 digits as base 10 numerals. The only differences are the choice of digits - regular polygons instead of an established set of digits like the Arabic digits - and the writing direction - increasing in scale, radially outwards instead of horizontally or vertically - defining the positional value of each digit.

Simply a dot moving around a circle once per day would have abandoned way more cultural assumption than this. Of course at the cost of making it harder to read precisely and looking less fancy.

This combination of base 60 and base 10 can also be understood as a multi-base numeral system. 12:34:56 can be understood as 123456 with non-uniform positional values 1, 10, 60, 600, 3,600, 36,000 from right to left directly yielding the number of seconds since midnight as 1 x 36,000 + 2 x 3,600 + 3 x 600 + 4 x 60 + 5 x 10 + 6 x 1 = 45,296.

The polygon numerals are actually similar to Babylonian cuneiform numerals [1]. They use a positional system just like Hindu-Arabic numerals with the positional value increasing by a factor of the base - 10 for Hindu-Arabic numerals, 60 for Babylonian cuneiform numerals - from right to left but there are not different digits 0 to 9 - or actually 0 to 59 because of base 60 - but they just repeat a symbol for one (I) [2] n times like the Roman numerals do. This IIII II is 42 but in base 60, so 4 x 60^1 + 2 x 60^0 = 242. Ignoring the edges, the polygon numerals express the digit value by repeating a vertex 0 to 9 times and each scale increase of the polygon adds a factor according to the 60 and 10 multi-base representation described above.

[1] https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals

[2] Because repeating the symbol for one (I) up to 59 times is inconvenient, they have a symbol for ten (<) as a shortcut, just as the Roman numerals have V for IIIII. <II <<<IIII is (1 x 10 + 2 x 1) x 60^1 + (3 x 10 + 4 x 1) x 60^0 = 754.