What is a thorpe?

Thorpe

The -thorpe comes from octothorpe. Its origins are unknown. The other words are rare and likely variations after octothorpe.

Octothorpe

The OED says of octothorpe:

The term was reportedly coined in the early 1960s by Don Macpherson, an employee of Bell Laboratories:

1996 Telecom Heritage No. 28. 53 His thought process was as follows: There are eight points on the symbol so octo should be part of the name. We need a few more letters or another syllable to make a noun... (Don Macpherson..was active in a group that was trying to get Jim Thorpe's Olympic medals returned from Sweden). The phrase thorpe would be unique.

For an alternative explanation see quot. 1996; in a variant of this explanation, the word is explained as arising from the use of the symbol in cartography to represent a village.

For a different explanation from a former employee of Bell Laboratories, arguing that the word is a completely arbitrary formation (and that it originally had the form octatherp) see D. A. Kerr ‘The ASCII Character Octatherp’ in http://doug.kerr.home.att.net (2006).

Quot. 1996 is:

1996 New Scientist 30 Mar. 54/3 The term ‘octothorp(e)’ (which MWCD10 dates 1971) was invented for ‘#’, allegedly by Bell Labs engineers when touch-tone telephones were introduced in the mid-1960s. ‘Octo-’ means eight, and ‘thorp’ was an Old English word for village: apparently the sign was playfully construed as eight fields surrounding a village.

Hexathorpe, quadrathorpe and duothorpe

Hexathorpe, quadrathorpe and duothorpe don't appear in the OED and I suspect they're variations after octothorpe. They also don't figure in this Google Ngrams chart and a quick search of Usenet shows they're usually mentioned in reference to the octothorpe.

Wikitionary specifically says the etymology of octothorpe is unclear and disputed, but one contender is:

In cartography, the octothorp (#) is a traditional symbol for village: eight fields around a central square.

From octo- (“eight”) and thorpe (“field, hamlet or small village”).

That is the source of its name. Octothorp means eight fields.

Which is as plausible as any of the other candidate etymologies, and more satisfying (the others being intentional, and uninteresting, jocular coinages).