[{item:"journal",qty:25,tags:["blank","red"],dim_cm:[14,21]},{item:"notebook",qty:50,tags:["red","blank"],dim_cm:[14,21]},{item:"paper",qty:100,tags:["red","blank","plain"],dim_cm:[14,21]},{item:"planner",qty:75,tags:["blank","red"],dim_cm:[22.85,30]},{item:"postcard",qty:45,tags:["blue"],dim_cm:[10,15.25]}]

db.collection.aggregate([{$unwind:"$tags"},{$group:{_id:null,tags:{"$addToSet":"$tags"},dim_cm:{"$addToSet":"$dim_cm"}}},{$unwind:"$dim_cm"},{$unwind:"$dim_cm"},{$group:{_id:null,tags:{"$first":"$tags"},dim_cm:{"$addToSet":"$dim_cm"}}}])