diff --git a/classes.cpp b/classes.cpp
index f7b9197b..8e40c091 100644
--- a/classes.cpp
+++ b/classes.cpp
@@ -722,7 +722,8 @@ enum eGeometry {
   gBinary4, gSol,
   gKiteDart2, gKiteDart3, gNil, gProduct, gRotSpace,
   gTernary, gNIH, gSolN, gInfOrder, gSpace336, gSpace344, gCrystal344,
-  gArnoldCat, gArbitrary, gInfOrder4,
+  gArnoldCat, gArbitrary, gInfOrder4, gCrystal534,
+  gSpace535, gSpace536,
   gGUARD};
 
 enum eGeometryClass { gcHyperbolic, gcEuclid, gcSphere, gcSolNIH, gcNil, gcProduct, gcSL2 };
@@ -888,6 +889,9 @@ EX vector<geometryinfo> ginf = {
   {"cat",    "cat",     "Arnold's cat mapping torus",                 "cat",     12, 3, qBINARY | qSOL | qsBQ | qOPTQ, giSolNIH, 0x52200, {{6, 4}}, eVariation::pure},
   {"file",   "none",    "load from file",                             "file",     7, 3, qEXPERIMENTAL,  giEuclid2, 0, {{7, 5}}, eVariation::pure},
   {"{4,oo}", "none",    "{4,∞} (infinite squares)",                   "oox4",     4, OINF, qIDEAL,  giHyperb2, 0x49400, {{5, 5}}, eVariation::pure},
+  {"{5,3,4}","Crystal", "6D crystal in H3",                           "Cryst6" , 12, 4, qANYQ | qCRYSTAL, giHyperb3, 0x52000, {{7, 3}}, eVariation::pure},
+  {"{5,3,5}","none",    "{5,3,5} hyperbolic honeycomb",               "535",     12, 5, 0,         giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
+  {"{5,3,6}","none",    "{5,3,6} hyperbolic honeycomb",               "536",     12, 6, qIDEAL,    giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
   };
   // bits: 9, 10, 15, 16, (reserved for later) 17, 18
 
diff --git a/crystal.cpp b/crystal.cpp
index 113dc8fe..35193c42 100644
--- a/crystal.cpp
+++ b/crystal.cpp
@@ -361,20 +361,99 @@ int fiftyrule(coord c) {
 bool is_bi(crystal_structure& cs, coord co);
 
 #if MAXMDIM >= 4
-typedef array<coord, 8> shifttable;
+typedef array<coord, 12> shifttable;
+
+array<int, 6> ctable[64] = {
+   {0, 1, 2, 3, 4, 5, },
+   {6, 1, 5, 4, 3, 2, },
+   {0, 7, 5, 4, 3, 2, },
+   {6, 7, 2, 3, 4, 5, },
+   {0, 1, 5, 4, 3, 8, },
+   {6, 1, 8, 3, 4, 5, },
+   {0, 7, 8, 3, 4, 5, },
+   {6, 7, 5, 4, 3, 8, },
+   {0, 1, 5, 4, 9, 2, },
+   {6, 1, 2, 9, 4, 5, },
+   {0, 7, 2, 9, 4, 5, },
+   {6, 7, 5, 4, 9, 2, },
+   {0, 1, 8, 9, 4, 5, },
+   {6, 1, 5, 4, 9, 8, },
+   {0, 7, 5, 4, 9, 8, },
+   {6, 7, 8, 9, 4, 5, },
+   {0, 1, 5, 10, 3, 2, },
+   {6, 1, 2, 3, 10, 5, },
+   {0, 7, 2, 3, 10, 5, },
+   {6, 7, 5, 10, 3, 2, },
+   {0, 1, 8, 3, 10, 5, },
+   {6, 1, 5, 10, 3, 8, },
+   {0, 7, 5, 10, 3, 8, },
+   {6, 7, 8, 3, 10, 5, },
+   {0, 1, 2, 9, 10, 5, },
+   {6, 1, 5, 10, 9, 2, },
+   {0, 7, 5, 10, 9, 2, },
+   {6, 7, 2, 9, 10, 5, },
+   {0, 1, 5, 10, 9, 8, },
+   {6, 1, 8, 9, 10, 5, },
+   {0, 7, 8, 9, 10, 5, },
+   {6, 7, 5, 10, 9, 8, },
+   {0, 1, 11, 4, 3, 2, },
+   {6, 1, 2, 3, 4, 11, },
+   {0, 7, 2, 3, 4, 11, },
+   {6, 7, 11, 4, 3, 2, },
+   {0, 1, 8, 3, 4, 11, },
+   {6, 1, 11, 4, 3, 8, },
+   {0, 7, 11, 4, 3, 8, },
+   {6, 7, 8, 3, 4, 11, },
+   {0, 1, 2, 9, 4, 11, },
+   {6, 1, 11, 4, 9, 2, },
+   {0, 7, 11, 4, 9, 2, },
+   {6, 7, 2, 9, 4, 11, },
+   {0, 1, 11, 4, 9, 8, },
+   {6, 1, 8, 9, 4, 11, },
+   {0, 7, 8, 9, 4, 11, },
+   {6, 7, 11, 4, 9, 8, },
+   {0, 1, 2, 3, 10, 11, },
+   {6, 1, 11, 10, 3, 2, },
+   {0, 7, 11, 10, 3, 2, },
+   {6, 7, 2, 3, 10, 11, },
+   {0, 1, 11, 10, 3, 8, },
+   {6, 1, 8, 3, 10, 11, },
+   {0, 7, 8, 3, 10, 11, },
+   {6, 7, 11, 10, 3, 8, },
+   {0, 1, 11, 10, 9, 2, },
+   {6, 1, 2, 9, 10, 11, },
+   {0, 7, 2, 9, 10, 11, },
+   {6, 7, 11, 10, 9, 2, },
+   {0, 1, 8, 9, 10, 11, },
+   {6, 1, 11, 10, 9, 8, },
+   {0, 7, 11, 10, 9, 8, },
+   {6, 7, 8, 9, 10, 11, },
+   };
 
 shifttable get_canonical(coord co) {
   shifttable res;
-  for(int i=0; i<4; i++) {
-    res[i] = c0;
-    res[i][i] = 2;
-    res[i+4] = c0;
-    res[i+4][i] = -2;
+  if(S7 == 12) {
+    int eid = 0;
+    for(int a=0; a<6; a++) if(co[a] & 2) eid += (1<<a);
+    for(int i=0; i<12; i++) res[i] = c0;
+    for(int i=0; i<6; i++) {
+      int c = ctable[eid][i];
+      res[i][c % 6] = (c>=6) ? -2 : 2;
+      res[6+i][c % 6] = (c>=6) ? 2 : -2;
+      }
+    }
+  else {
+    for(int i=0; i<4; i++) {
+      res[i] = c0;
+      res[i][i] = 2;
+      res[i+4] = c0;
+      res[i+4][i] = -2;
+      }
+    for(int a=0; a<4; a++) if(co[a] & 2) swap(res[a], res[a+4]);
+    int bts = 0;
+    for(int a=0; a<4; a++) if(co[a] & 2) bts++;
+    if(bts & 1) swap(res[2], res[3]), swap(res[6], res[7]);
     }
-  for(int a=0; a<4; a++) if(co[a] & 2) swap(res[a], res[a+4]);
-  int bts = 0;
-  for(int a=0; a<4; a++) if(co[a] & 2) bts++;
-  if(bts & 1) swap(res[2], res[3]), swap(res[6], res[7]);
   return res;
   }
 #endif
@@ -407,7 +486,7 @@ struct hrmap_crystal : hrmap_standard {
   
   hrmap_crystal() {
 #if MAXMDIM >= 4
-    if(crystal3()) reg3::generate(), cs.dim = 4; else 
+    if(crystal3()) reg3::generate(), cs.dim = S7 / 2; else 
 #endif
     cs.build();
     
@@ -483,9 +562,9 @@ struct hrmap_crystal : hrmap_standard {
       auto h1 = get_heptagon_at(co1, S7);
       auto st1 = get_canonical(co1);
     
-      for(int d1=0; d1<8; d1++) if(st1[d1] == st[d])
-        h->c.connect(d, h1, d1 ^ 4, false);
-
+      for(int d1=0; d1<S7; d1++) if(st1[d1] == st[d])
+        h->c.connect(d, h1, (d1+S7/2) % S7, false);
+      
       return h1;
       }
     #endif
@@ -526,8 +605,8 @@ struct hrmap_crystal : hrmap_standard {
   transmatrix adj(heptagon *h, int d) override {
     auto co = hcoords[h];
     int id = 0;
-    for(int a=0; a<4; a++) id = (2*id) + ((co[a]>>1) & 1);
-    id = 8*id + d;
+    for(int a=0; a<S7/2; a++) id = (2*id) + ((co[a]>>1) & 1);
+    id = S7*id + d;
     if(adjs.count(id)) return adjs[id];
     transmatrix T = reg3::adjmoves[d];
     reg3::generate_cellrotations();
@@ -536,13 +615,20 @@ struct hrmap_crystal : hrmap_standard {
     auto st1 = get_canonical(co1);
     int qty = 0;
     transmatrix res;
+    ld gdist = S7 == 12 ? hdist0(tC0(reg3::adjmoves[0])) : reg3::strafedist;
+
     for(auto& cr: cgi.cellrotations) {
+
       transmatrix U = T * cr.first;
-      for(int s=0; s<8; s++) 
+      
+      ld go = hdist0(U * tC0(reg3::adjmoves[h->c.spin(d)]));
+      if(go > 1e-2) continue;
+
+      for(int s=0; s<S7; s++) 
         if(reg3::dirs_adjacent[d][s])
-          for(int t=0; t<8; t++) 
+          for(int t=0; t<S7; t++) 
             if(st1[t] == st[s]) {
-              if(hdist(U * tC0(reg3::adjmoves[t]), tC0(reg3::adjmoves[s])) > reg3::strafedist + .1)
+              if(hdist(U * tC0(reg3::adjmoves[t]), tC0(reg3::adjmoves[s])) > gdist + .1)
                 goto wrong;
               }
       res = U;
diff --git a/pattern2.cpp b/pattern2.cpp
index 9529aebc..7e7f2b3f 100644
--- a/pattern2.cpp
+++ b/pattern2.cpp
@@ -394,6 +394,7 @@ EX int fieldval_uniq(cell *c) {
     }
   else if(bt::in() || arcm::in() || nil || S3 >= OINF || (cgflags & qIDEAL)) return 0;
   else if(&currfp == &fp_invalid) return 0;
+  else if(geometry == gSpace535) return 0;
   else if(WDIM == 3) return c->master->fieldval;
   else if(ctof(c) || NONSTDVAR) return c->master->fieldval/S7;
   else {
diff --git a/reg3.cpp b/reg3.cpp
index 99fd222c..055f8c42 100644
--- a/reg3.cpp
+++ b/reg3.cpp
@@ -636,7 +636,7 @@ EX namespace reg3 {
         quotient_map = new hrmap_from_crystal;
         h.zebraval = quotient_map->allh[0]->zebraval;
         }
-      if(hyperbolic && !(cgflags & qIDEAL)) {
+      if(hyperbolic && !(cgflags & qIDEAL) && geometry != gSpace535) {
         quotient_map = new hrmap_field3;
         h.zebraval = quotient_map->allh[0]->zebraval;
         }
@@ -945,7 +945,7 @@ EX bool pseudohept(cell *c) {
     return c->master->distance & 1;
   if(geometry == gField534) 
     return hr::celldistance(c, currentmap->gamestart()) & 1;
-  if(geometry == gCrystal344)
+  if(geometry == gCrystal344 || geometry == gCrystal534)
     return false;
   if(hyperbolic) {
     heptagon *h = m->reg_gmatrix[c->master].first;