Nesting partner
The partner you share a home with — used specifically to describe the cohabiting relationship without implying ranked hierarchy.
Nesting partner names the partner you live with. The word picks out one specific dimension of relationship-entwinement — co-habitation — without making claims about emotional ranking. A person can have a nesting partner and also have other deeply committed partners they do not live with; the term keeps those claims separate.
The advantage of nesting-partner language is precision. In hierarchical polyamory, the word primary tends to mean a bundle of things (you live together, your finances are merged, you are each other's most important person, your relationship takes precedence) that may not actually travel together. Nesting partner picks out the household-sharing part specifically. A nesting partner is, by definition, the person you do dishes with; whether they are also your most important person is a separate question.
Multiple-nesting arrangements exist. A triad living together has three nesting partners; a polycule of four sharing a home has four. Nesting-partner status is structurally a description of who is on the lease, who shares the kitchen, who handles the weekly grocery run. It is shaped by logistics as much as by emotional priority.
Solo polyamorous practitioners explicitly do not have nesting partners by design — autonomy and a separately-organised home are core to the structure. Some practitioners have nesting partners who are not romantic partners (deep platonic co-habitation), which the language accommodates without strain.