diff --git a/arbitrile.cpp b/arbitrile.cpp
index 614cf43b..bb00956c 100644
--- a/arbitrile.cpp
+++ b/arbitrile.cpp
@@ -1396,11 +1396,7 @@ geometryinfo1& arbi_tiling::get_geometry() {
   return ginf[gEuclid].g;
   }
 
-map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
-
-EX map<heptagon*, pair<heptagon*, transmatrix>> arbi_matrix;
-
-EX hrmap *current_altmap;
+EX backed_map bm;
 
 heptagon *build_child(heptspin p, pair<int, int> adj);
 
@@ -1539,30 +1535,12 @@ struct hrmap_arbi : hrmap {
     origin->s = hsOrigin;
     origin->c7 = newCell(origin->type, origin);
 
-    heptagon *alt = NULL;
-    
-    if(mhyperbolic) {
-      dynamicval<eGeometry> g(geometry, gNormal); 
-      alt = init_heptagon(S7);
-      alt->s = hsOrigin;
-      alt->alt = alt;
-      current_altmap = newAltMap(alt); 
-      }
-    
-    transmatrix T = lxpush(.01241) * spin(1.4117) * lxpush(0.1241) * Id;
-    arbi_matrix[origin] = make_pair(alt, T);
-    altmap[alt].emplace_back(origin, T);
+    bm.initialize(origin);
     }
 
   ~hrmap_arbi() {
     clearfrom(origin);
-    altmap.clear();
-    arbi_matrix.clear();
-    if(current_altmap) {
-      dynamicval<eGeometry> g(geometry, gNormal);       
-      delete current_altmap;
-      current_altmap = NULL;
-      }
+    bm.clear();
     }
   void verify() override { }
 
@@ -1619,34 +1597,24 @@ struct hrmap_arbi : hrmap {
       return h1;
       }
 
-    const auto& p = arbi_matrix[h];
+    const auto& p = bm.where[h];
     
     heptagon *alt = p.first;
     
     transmatrix T = p.second * adj(h, d);
     
-    if(mhyperbolic) {
-      dynamicval<eGeometry> g(geometry, gNormal); 
-      dynamicval<hrmap*> cm(currentmap, current_altmap);
-      // transmatrix U = T;
-      current_altmap->virtualRebase(alt, T);
-      // U = U * inverse(T);
-      }
+    transmatrix U;
+    bm.rebase(alt, T, U);
     fixmatrix(T);
 
-    if(meuclid) {
-      /* hash the rough coordinates as heptagon* alt */
-      size_t s = size_t(T[0][LDIM]+.261) * 124101 + size_t(T[1][LDIM]+.261) * 82143;
-      alt = (heptagon*) s;
-      }
-
-    for(auto& p2: altmap[alt]) if(id_of(p2.first) == co.sid) {
+    for(auto& p2: bm.what_at[alt]) if(id_of(p2.first) == co.sid) {
       connection_t co1 = co;
       if(find_connection(T, p2.second, co1)) {
         if(p2.first->move(co1.eid)) {
           throw hr_exception("already connected!");
           }
         h->c.connect(d, p2.first, co1.eid, co1.mirror);
+        bm.handle_precision_errors(p2.first);
         return p2.first;
         }
       }
@@ -1658,8 +1626,7 @@ struct hrmap_arbi : hrmap {
     h1->emeraldval = h->emeraldval ^ co.mirror;
     h->c.connect(d, h1, co.eid, co.mirror);
     
-    arbi_matrix[h1] = make_pair(alt, T);
-    altmap[alt].emplace_back(h1, T);    
+    bm.assign(h1, alt, T);
     return h1;
     }
   
@@ -2262,11 +2229,7 @@ EX void swap_vertices() {
   }
 
 #if MAXMDIM >= 4
-auto hooksw = addHook(hooks_swapdim, 100, [] {
-  swap_vertices();
-  for(auto& p: altmap) for(auto& pp: p.second) swapmatrix(pp.second);
-  for(auto& p: arbi_matrix) swapmatrix(p.second.second);
-  });
+auto hooksw = addHook(hooks_swapdim, 100, [] { swap_vertices(); bm.swapdim(); });
 #endif
 
 EX bool support_dice(int x) {
diff --git a/archimedean.cpp b/archimedean.cpp
index f8c03274..f4f403b3 100644
--- a/archimedean.cpp
+++ b/archimedean.cpp
@@ -560,11 +560,7 @@ ld archimedean_tiling::scale() {
   return edgelength;
   }
 
-map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
-
-EX map<heptagon*, pair<heptagon*, transmatrix>> archimedean_gmatrix;
-
-EX hrmap *current_altmap;
+EX backed_map bm;
 
 heptagon *build_child(heptspin p, pair<int, int> adj);
 
@@ -576,20 +572,6 @@ void connectHeptagons(heptspin hi, heptspin hs);
 /** @brief should we use gmatrix to compute relative_matrix faster? (not while in fake Archimedean) */
 EX bool use_gmatrix = true;
 
-/** @brief like adj, but in pure 
- *  not used by arcm itself, but used in fake arcm
- */
-
-EX geometry_information *alt_cgip[2];
-
-EX geometry_information *find_alt_cgip() {
-  auto& galt_cgip = alt_cgip[embedded_plane];
-  if(galt_cgip) return galt_cgip;
-  check_cgi();
-  cgi.require_basics();
-  return galt_cgip = cgip;
-  }
-
 struct hrmap_archimedean : hrmap {
   map<gp::loc, struct cdata> eucdata;
   heptagon *origin;
@@ -605,30 +587,8 @@ struct hrmap_archimedean : hrmap {
     parent_index_of(origin) = DUAL ? 1 : 0;
     id_of(origin) = id;
     origin->c7 = newCell(N0/DUALMUL, origin);
-    
-    heptagon *alt = NULL;
-    
-    if(hyperbolic) {
-      bool f = geom3::flipped;
-      if(f) geom3::light_flip(false);
-      if(1) {
-        dynamicval<eGeometry> g(geometry, gNormal);
-        dynamicval<eVariation> gv(variation, eVariation::pure);
-        dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
-        alt = init_heptagon(S7);
-        alt->s = hsOrigin;
-        alt->alt = alt;
-        current_altmap = newAltMap(alt);
-        }
-      if(f) geom3::light_flip(true);
-      }
 
-    bool f = geom3::flipped;
-    if(f) geom3::light_flip(false);
-    transmatrix T = lxpush(.01241) * spin(1.4117) * lxpush(0.1241) * Id;
-    if(f) geom3::light_flip(true);
-    archimedean_gmatrix[origin] = make_pair(alt, T);
-    altmap[alt].emplace_back(origin, T);
+    bm.initialize(origin);
   
     if(current.real_faces == 0 && DUAL) {
       heptspin hs(origin, 0);
@@ -646,7 +606,7 @@ struct hrmap_archimedean : hrmap {
       for(int s=2; s<2*current.N; s+=2) {
         heptspin hs(o0, s);
         heptagon *hnew = build_child(hs, current.get_adj(hs));
-        // no need to specify archimedean_gmatrix and altmap
+        // no need to specify where and what_at
         hnew->c.connect(1, heptspin(o1, 2*current.N-s));
         }
       o1->c.connect(1, o0, 2*current.N-1, false);
@@ -663,16 +623,9 @@ struct hrmap_archimedean : hrmap {
 
   ~hrmap_archimedean() {
     clearfrom(origin);
-    altmap.clear();
-    archimedean_gmatrix.clear();
-    if(current_altmap) {
-      dynamicval<eGeometry> g(geometry, gNormal);       
-      dynamicval<eVariation> gv(variation, eVariation::pure);
-      dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
-      delete current_altmap;
-      current_altmap = NULL;
-      }
+    bm.clear();
     }
+
   void verify() override { }
 
   heptagon *create_step(heptagon *h, int d) override {
@@ -702,33 +655,18 @@ struct hrmap_archimedean : hrmap {
   
     // * spin(-tri[id][pi+i].first) * lxpush(t.second) * pispin * spin(tri[id'][p'+d'].first)
 
-    auto& p1 = archimedean_gmatrix[h];
-    
-    heptagon *alt = p1.first;
-  
+    auto& p1 = bm.where[h];
+
+    heptagon *alt = p1.first; auto alt0 = alt;
+
     transmatrix T = p1.second * spin(-t1.first) * lxpush(t1.second);
     transmatrix U = Id;
 
-    if(hyperbolic) {
-      dynamicval<int> uc(cgip->use_count, cgip->use_count+1);
-      dynamicval<eGeometry> g(geometry, gNormal);
-      dynamicval<eVariation> gv(variation, eVariation::pure);
-      dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
-      dynamicval<hrmap*> cm(currentmap, current_altmap);
-      U = T;
-      current_altmap->virtualRebase(alt, T);
-      U = U * iso_inverse(T);
-      }
-    
-    if(euclid) {
-      /* hash the rough coordinates as heptagon* alt */
-      size_t s = size_t(T[0][LDIM]+.261) * 124101 + size_t(T[1][LDIM]+.261) * 82143;
-      alt = (heptagon*) s;
-      }
-      
+    bm.rebase(alt, T, U);
+
     if(debug_geometry) println(hlog, "look for: ", alt, " / ", kz(T * C0));
-  
-    for(auto& p2: altmap[alt]) if(same_point_may_warn(p2.second * tile_center(), T * tile_center())) {
+
+    for(auto& p2: bm.what_at[alt]) if(same_point_may_warn(p2.second * tile_center(), T * tile_center())) {
       if(debug_geometry) println(hlog, "cell found: ", p2.first);
       for(int d2=0; d2<p2.first->degree(); d2++) {
         heptspin hs(p2.first, d2);
@@ -742,14 +680,17 @@ struct hrmap_archimedean : hrmap {
           // p1.second * spinm(-t1.first) * lxpush(t1.second) * spin(pi+t2.first) == p2.second
           
           // bring p1 and p2 closer, to prevent floating point errors
-          if(hyperbolic) {
+          if(hyperbolic && false) {
             fixup_matrix(p1.second, U * p2.second * spin(-M_PI - t2.first) * lxpush(-t1.second) * spin(t1.first), 0.25);
             fixup_matrix(p2.second, T1, 0.25);
+            for(auto& z: bm.what_at[alt0]) if(z.first == h) z.second = p1.second;
+            bm.where[p2.first].second = p2.second;
             }
   
           while(skip_digons(hs, -1)) hs--;
           connectHeptagons(hi, hs);
           connect_digons_too(hi, hs);
+          bm.handle_precision_errors(h);
           return h->move(d);
           }
         }
@@ -761,8 +702,7 @@ struct hrmap_archimedean : hrmap {
     fixmatrix(T1);
   
     heptagon *hnew = build_child(hi, current.get_adj(hi));
-    altmap[alt].emplace_back(hnew, T1);
-    archimedean_gmatrix[hnew] = make_pair(alt, T1);
+    bm.assign(hnew, alt, T1);
     connect_digons_too(hi, heptspin(hnew, 0));
     
     return hnew;
@@ -797,7 +737,13 @@ struct hrmap_archimedean : hrmap {
       }
     }
 
+  transmatrix adj(heptagon *h, int dir) override {
+    return current_or_fake().adjcell_matrix(h, dir);
+    }
+
   transmatrix adj(cell *c, int dir) override {
+    if(!PURE) for(int i=0; i<c->master->type; i++) if(c->master->move(i) == c->cmove(dir)->master)
+      return adj(c->master, i);
     return calc_relative_matrix(c->cmove(dir), c, C0);
     }
   
@@ -925,7 +871,7 @@ heptagon *build_child(heptspin p, pair<int, int> adj) {
     }
   else
     h->fieldval = -100;
-  h->fiftyval = isize(archimedean_gmatrix);
+  h->fiftyval = isize(bm.where);
   if(p.at->s == hsOrigin)
     h->rval1 = 1 + (p.spin % 2);
   else {
@@ -949,7 +895,7 @@ void connect_digons_too(heptspin h1, heptspin h2) {
   if(skip_digons(h1, -1)) {
     h1--, h2++;
     heptagon *hnew = build_child(h1, current.get_adj(h1));
-    // no need to specify archimedean_gmatrix and altmap
+    // no need to specify where and what_at
     hnew->c.connect(1, h2);
     h1--, h2++;
     if(debug_archimedean_map) println(hlog, hr::format("OL2 %p.%d ~ %p.%d\n", hr::voidp(h1.at), h1.spin, hr::voidp(h2.at), h2.spin));
@@ -1131,7 +1077,7 @@ int readArgs() {
 #if CAP_COMMANDLINE
 auto hook = 
   addHook(hooks_args, 100, readArgs)
-+ addHook(hooks_gamedata, 0, [] (gamedata* gd) { gd->store(altmap); gd->store(archimedean_gmatrix); gd->store(current_altmap); });
++ addHook(hooks_gamedata, 0, [] (gamedata* gd) { bm.store(gd); });
 
 #endif
 
@@ -1139,20 +1085,7 @@ auto hook =
 auto hooksw = addHook(hooks_swapdim, 100, [] {
 
   if(!arcm::in()) return;
-
-  dynamicval<eGeometry> g(geometry, gNormal);
-  dynamicval<eVariation> gv(variation, eVariation::pure);
-
-  alt_cgip[0] = nullptr;
-  alt_cgip[1] = nullptr;
-
-  dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
-
-  for(auto& p: altmap) for(auto& pp: p.second) swapmatrix(pp.second);
-  for(auto& p: archimedean_gmatrix) swapmatrix(p.second.second);
-
-  alt_cgip[0] = nullptr;
-  alt_cgip[1] = nullptr;
+  bm.swapdim();
   });
 #endif
 
diff --git a/cell.cpp b/cell.cpp
index 2ed87a29..6158e94a 100644
--- a/cell.cpp
+++ b/cell.cpp
@@ -1273,12 +1273,12 @@ int ld_to_int(ld x) {
 
 #if CAP_ARCM
 EX gp::loc pseudocoords(cell *c) {
-  transmatrix T = arcm::archimedean_gmatrix[c->master].second;
+  transmatrix T = arcm::bm.where[c->master].second;
   return {ld_to_int(T[0][LDIM]), ld_to_int((spin(60._deg) * T)[0][LDIM])};
   }
 
 EX cdata *arcmCdata(cell *c) {
-  auto &agm = arcm::archimedean_gmatrix;
+  auto &agm = arcm::bm.where;
   if(!agm.count(c->master) || !agm[c->master].first) {
     forCellEx(c1, c) if(agm.count(c->master) && agm[c->master].first) return arcmCdata(c1);
     static cdata dummy;
@@ -1286,7 +1286,7 @@ EX cdata *arcmCdata(cell *c) {
     }
   heptagon *h2 = agm[c->master].first;
   dynamicval<eGeometry> g(geometry, gNormal); 
-  dynamicval<hrmap*> cm(currentmap, arcm::current_altmap);  
+  dynamicval<hrmap*> cm(currentmap, arcm::bm.current_altmap);
   return getHeptagonCdata(h2);
   }
 #endif
diff --git a/geometry.cpp b/geometry.cpp
index d4d69646..c2c21bac 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -1474,8 +1474,8 @@ EX void check_cgi() {
   if(mhybrid) hybrid::underlying_cgip->timestamp = ntimestamp;
   if(fake::in() || (mhybrid && PIU(fake::in()))) fake::underlying_cgip->timestamp = ntimestamp;
   #if CAP_ARCM
-  if(arcm::alt_cgip[0]) arcm::alt_cgip[0]->timestamp = ntimestamp;
-  if(arcm::alt_cgip[1]) arcm::alt_cgip[1]->timestamp = ntimestamp;
+  if(arcm::bm.alt_cgip[0]) arcm::bm.alt_cgip[0]->timestamp = ntimestamp;
+  if(arcm::bm.alt_cgip[1]) arcm::bm.alt_cgip[1]->timestamp = ntimestamp;
   #endif
   
   int limit = 3;
diff --git a/hyper.cpp b/hyper.cpp
index a9c080da..ce55affb 100644
--- a/hyper.cpp
+++ b/hyper.cpp
@@ -38,6 +38,7 @@
 #include "asonov.cpp"
 #include "kite.cpp"
 #include "aperiodic-hat.cpp"
+#include "backed-map.cpp"
 #include "archimedean.cpp"
 #include "arbitrile.cpp"
 #include "rulegen.cpp"