Halliday & Matthiessen (2014: 395-6):
In expressions of facet such as the front of the house, the entire length of the narrative, the Head noun front, length is related in function to the preposition in a prepositional phrase: before/in front of the house, throughout the narrative. There is, in fact, a cline from one to the other: for example
- at the summit of the hill (where summit is both Head and Thing) –
- at/on the top of the hill –
- on top of the hill –
- (atop the hill —)
- on the hill (where hill is both Head and Thing).
In on top of the hill, on top of is a preposition group; here top has no Deictic, cannot be pluralised, and can be used with abstract Things (I think we’ve got on top of the problem). But at/on the top of the hill forms a prepositional phrase: the preposition is at or on; the top of the hill is the Complement, where top can be pluralised ((on) the tops of the hills), but not made abstract – we will not find on the top(s) of the problem(s). Here top is a facet term, and the analysis will be as in Figure 6-12.
In Figure 6-12, 'Qualifier' (experiential) should be 'Postmodifier' (logical).