diff --git a/cell.cpp b/cell.cpp
index 1c2cd0e1..c1526764 100644
--- a/cell.cpp
+++ b/cell.cpp
@@ -85,6 +85,11 @@ struct hrmap {
 
   /** \brief in 3D honeycombs, returns a vector<bool> v, where v[j] iff faces i and j are adjacent */
   const vector<char>& dirdist(cellwalker cw) { return get_cellshape(cw.at).dirdist[cw.spin]; }
+
+  /** \brief the sequence of heptagon movement direction to get from c->master to c->move(i)->master; implemented only for reg3 */
+  virtual const vector<int>& get_move_seq(cell *c, int i) {
+    throw hr_exception("get_move_seq not implemented for this map class");
+    }
   };
 
 /** hrmaps which are based on regular non-Euclidean 2D tilings, possibly quotient  
diff --git a/fake.cpp b/fake.cpp
index 2de620f3..efd8a729 100644
--- a/fake.cpp
+++ b/fake.cpp
@@ -34,7 +34,7 @@ EX namespace fake {
     if(arcm::in() && PURE) return true;
     if(WDIM == 2) return false;
     if(among(geometry, gBitrunc3)) return false;
-    if(reg3::in() && !among(variation, eVariation::pure, eVariation::subcubes)) return false;
+    if(reg3::in() && !among(variation, eVariation::pure, eVariation::subcubes, eVariation::coxeter)) return false;
     return euc::in() || reg3::in();
     }
   
@@ -87,18 +87,25 @@ EX namespace fake {
     transmatrix adj(cell *c, int d) override {
       transmatrix S1, S2;
       ld dist;
-      if(variation == eVariation::subcubes && c->master == c->cmove(d)->master) {
-        auto& s1 = get_cellshape(c);
-        auto& s2 = get_cellshape(c->move(d));
-        return s1.from_cellcenter * s2.to_cellcenter;
+      bool impure = reg3::in() && !PURE;
+      vector<int> mseq;
+      if(impure) {
+        mseq = FPIU ( currentmap->get_move_seq(c, d) );
+        if(mseq.empty()) {
+          auto& s1 = get_cellshape(c);
+          auto& s2 = get_cellshape(c->move(d));
+          return s1.from_cellcenter * s2.to_cellcenter;
+          }
+        if(isize(mseq) > 1)
+          throw hr_exception("fake adj not implemented for isize(mseq) > 1");
         }
-      in_underlying([c, d, &S1, &S2, &dist] {
+      in_underlying([c, d, &S1, &S2, &dist, &impure, &mseq] {
         #if CAP_ARCM
         dynamicval<bool> u(arcm::use_gmatrix, false);
         #endif
         transmatrix T;
-        if(variation == eVariation::subcubes) {
-          T = currentmap->adj(c->master, d);
+        if(impure) {
+          T = currentmap->adj(c->master, mseq[0]);
           }
         else {
           T = currentmap->adj(c, d);
@@ -109,7 +116,7 @@ EX namespace fake {
         S2 = xpush(-dist) * T1;
         });
       
-      if(variation == eVariation::subcubes) {
+      if(impure) {
         auto& s1 = get_cellshape(c);
         auto& s2 = get_cellshape(c->move(d));
         S1 = s1.from_cellcenter * S1;
diff --git a/reg3.cpp b/reg3.cpp
index 46e49f95..41a106d4 100644
--- a/reg3.cpp
+++ b/reg3.cpp
@@ -717,6 +717,11 @@ EX namespace reg3 {
       int id = local_id.at(cw.at).first;
       return cellwalker(cw.at->cmove(j), strafe_data[id][j][cw.spin]);
       }
+
+    const vector<int>& get_move_seq(cell *c, int i) override {
+      int id = local_id.at(c).first;
+      return move_sequences[id][i];
+      }
     };
 
   struct hrmap_quotient3 : hrmap_closed3 { };
@@ -2022,6 +2027,11 @@ EX namespace reg3 {
       if(PURE && res1 != res2) println(hlog, "h3: ", res1, " vs ", res2);
       return res2;
       }
+
+    const vector<int>& get_move_seq(cell *c, int i) override {
+      int aid = cell_id.at(c);
+      return quotient_map->get_move_seq(quotient_map->acells[aid], i);
+      }
     };
 
   struct hrmap_h3_rule_alt : hrmap {