Is there any regularity in the meter of Robin Hyde's poem "An Absent Face"?Robin Hyde: from Houses by the sea, The Beaches III An Absent Face An...

There definitely is regularity in "An Absent Face" by New Zealander Robin Hyde. There is also irregularity where Hyde varies the base rhythm and meter with opposing rhythm and meter. The poem starts out in iambic (^/) pentameter, which is five metrical feet of one unstressed count followed by one stressed count (^/):

An^ ab' / -sent^ face', / re^ -mote' / and^ sharp', / as^ far'

The third line varies this pattern by adding an incomplete end foot creating iambic hexameter. Lines four and five pick up the original iambic pentameter, with an elision of an unaccented syllable in "different" to render "diff'rent" in the last foot of the fourth line.

Line six varies quite a bit to accommodate "Ganges" and "Juma," both of which have accented first syllables. The result is two feet of dactyls (/^^) followed by three feet of trochees (/^), though still in pentameter. In addition, the second foot makes use of an oft overlooked component of English poetry and incorporates a pause, denoted by the comma, as a rightful part of the rhythmic structure.

Gan' -ges^ and^ / Jum' -na^,^ / half' the^ / par' -rot’s^ / pla' -ces^

Line seven repeats the pattern of line three with iambic hexameter and an incomplete end foot. Lines eight and nine reestablish the base iambic pentameter, but line ten reverses that with a trochaic pentameter with an incomplete end foot:

Ra' -ges^, / fiz' -zles^ / red' at^ / ev' -ery^ / one'.

Line eleven echoes line ten, iambic pentameter with and incomplete end foot. Lines twelve, thirteen, and fourteen return to the base pattern of iambic pentameter. Line fifteen is awkward.

The one ahead of it, line fourteen, ends with an enjambment and an newly begun thought ("but one") broken short to be picked up on line fifteen with "Thinks your ... ." This line is problematic because it can be scanned one of two ways.

It can be scanned as iambic: Think^ your' / clean ^ tooth' / -brush^, home' / -work^ neat' / -ly^ done' . Or it can be scanned in keeping with Hyde's other variation patterns: Think' your^ clean^ / tooth' -brush^ / home' -work^ / neat' -ly^ / done'.

When scansion is emphasized, it may be more neatly scanned as iambs. However when the thought is emphasized, "but one thinks, your clean toothbrush, homework neatly done," said in conjunction with asking questions of the stooping shadows of line thirteen, then the variation of combined dactyls and trochees makes more sense, particularly when the line then echoes Hyde's other variations, even having an incomplete end trochaic foot:

Think' your^ clean^ / tooth' -brush^ / home' -work^ / neat' -ly^ / done'

Line sixteen is varied by having iambic tetrameter (four feet), with an elision between "say" and "A" on an unaccented count in the second foot. Lines seventeen and eighteen return to the base pattern of iambic pentameter, with no variations.
So then, yes, there is regularity while there is also systematic variation of the regular pattern.