diff --git a/archimedean.cpp b/archimedean.cpp
index 34803a46..f04feb4f 100644
--- a/archimedean.cpp
+++ b/archimedean.cpp
@@ -438,7 +438,7 @@ struct hrmap_archimedean : hrmap {
 
     parent_index_of(origin) = DUAL ? 1 : 0;
     id_of(origin) = id;
-    origin->c7 = newCell(DUAL ? N0/2 : N0, origin);
+    origin->c7 = newCell(N0/DUALMUL, origin);
     
     heptagon *alt = NULL;
     
@@ -517,7 +517,7 @@ heptagon *build_child(heptspin p, pair<int, int> adj) {
   id_of(h) = adj.first;
   parent_index_of(h) = adj.second;
   int nei = neighbors_of(h);
-  h->c7 = newCell(DUAL ? nei/2 : nei, h);
+  h->c7 = newCell(nei/DUALMUL, h);
   h->distance = p.at->distance + 1;
   if(adj.first < 2*current.N && !DUAL) {
     int s = 0;
diff --git a/cell.cpp b/cell.cpp
index b1ff475a..7a04ecd5 100644
--- a/cell.cpp
+++ b/cell.cpp
@@ -1259,7 +1259,7 @@ cdata *getHeptagonCdata(heptagon *h) {
   cdata mydata = *getHeptagonCdata(h->move(0));
 
   for(int di=3; di<5; di++) {
-    heptspin hs; hs.at = h; hs.spin = di;
+    heptspin hs(h, di, false);
     int signum = +1;
     while(true) {
       heptspin hstab[15];
diff --git a/complex.cpp b/complex.cpp
index 5445cea6..10a7e9a3 100644
--- a/complex.cpp
+++ b/complex.cpp
@@ -1155,7 +1155,7 @@ namespace mirror {
       heptspin hs1 = hs + i;
       if(lev == 0) {
         if(hs1.at != hs0.at && equal(hs1, hs0, 3)) {
-          createMirror(cellwalker(hs1.at->c7, hs1.spin, hs1.mirrored), cpid);
+          createMirror(hs1 + cth, cpid);
           result++;
           }
         }
@@ -1165,7 +1165,7 @@ namespace mirror {
     }
 
   void create_archimedean(cellwalker cw, int cpid, bool mirrored) {
-    heptspin hs(cw.at->master, cw.spin, cw.mirrored);
+    heptspin hs = cw + cth;
     heptspin hsx = hs;
     if(mirrored) hsx += wmirror;
     if(create_archimedean_rec(hsx, cpid, hs, 2)) return;
@@ -1185,9 +1185,7 @@ namespace mirror {
     
     if(GOLDBERG) {
       for(int i=0; i<cw.at->type; i++) {
-        heptspin hs(cw.at->master, cw.spin, cw.mirrored);
-        hs = hs + i + wstep + i - (gp::param.first == gp::param.second ? 1 : 0);
-        createMirror(cellwalker(hs.at->c7, hs.spin, hs.mirrored), cpid);
+        createMirror(cw + cth + i + wstep + i - (gp::param.first == gp::param.second ? 1 : 0) + cth, cpid);
         }
       return;
       }
@@ -1206,17 +1204,13 @@ namespace mirror {
       }
     if(GOLDBERG && !(S7 & 1)) {
       for(int i=0; i<cw.at->type; i++) {
-        heptspin hs(cw.at->master, cw.spin, cw.mirrored);
-        hs = hs + i + wstep + 1 + wstep + 1 + (S7/2) - i + 1;
-        createMirror(cellwalker(hs.at->c7, hs.spin, hs.mirrored), cpid);
+        createMirror(cw + cth + i + wstep + 1 + wstep + 1 + (S7/2) - i + 1 + cth, cpid);
         }
       return;
       }
     if(GOLDBERG && (S7 & 1)) {
       for(int i=0; i<cw.at->type; i++) {
-        heptspin hs(cw.at->master, cw.spin, cw.mirrored);
-        hs = hs + i + wstep + (S7/2) + wstep - 2 + wstep + (S7/2) - i;
-        createMirror(cellwalker(hs.at->c7, hs.spin, hs.mirrored), cpid);
+        createMirror(cw + cth + i + wstep + (S7/2) + wstep - 2 + wstep + (S7/2) - i + cth, cpid);
         }
       return;
       }
@@ -3201,9 +3195,7 @@ namespace windmap {
       auto &v = neighbors.back();
       if(NONSTDVAR && !sphere && !archimedean)
         for(int l=0; l<S7; l++) {
-          heptspin hs(cw.at->master, cw.spin);
-          hs = hs + l + wstep;
-          v.push_back(getId(cellwalker(hs.at->c7, hs.spin)));
+          v.push_back(getId(cw + cth + l + wstep + cth));
           }
       else
         for(int l=0; l<cw.at->type; l++) v.push_back(getId(cw+l+wstep));
diff --git a/geometry2.cpp b/geometry2.cpp
index aa63d6b8..1a92585a 100644
--- a/geometry2.cpp
+++ b/geometry2.cpp
@@ -515,7 +515,7 @@ hyperpoint farcorner(cell *c, int i, int which) {
       return spin(-t.first - M_PI / c->type) * xpush(ac.inradius[id/2] + ac.inradius[id1/2]) * xspinpush0(M_PI + M_PI/n1*(which?3:-3), ac.circumradius[id1/2]);
       }
     if(BITRUNCATED || DUAL) {
-      int mul = DUAL ? 2 : 1;
+      int mul = DUALMUL;
       auto &ac = arcm::current;
       auto adj = ac.get_adj(c->master, i * mul);
       heptagon h; cell cx; cx.master = &h;
diff --git a/hyper.h b/hyper.h
index 96f16443..5244d315 100644
--- a/hyper.h
+++ b/hyper.h
@@ -538,6 +538,10 @@ int heptagon::degree() { if(archimedean) return arcm::degree(this); else return
 typedef walker<heptagon> heptspin;
 typedef walker<cell> cellwalker;
 
+static const struct cth_t { cth_t() {}} cth;
+heptspin operator+ (cellwalker cw, cth_t) { return heptspin(cw.at->master, cw.spin * DUALMUL, cw.mirrored); }
+cellwalker operator+ (heptspin hs, cth_t) { return cellwalker(hs.at->c7, hs.spin / DUALMUL, hs.mirrored); }
+
 #define BUGCOLORS 3
 
 // land completion for shared unlocking
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 40707764..ff5c2de8 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -807,7 +807,7 @@ void optimizeview() {
   if(binarytiling || archimedean) {
     turn = -1, best = View[2][2];
     for(int i=0; i<viewctr.at->c7->type; i++) {
-      int i1 = i * (DUAL ? 2 : 1);
+      int i1 = i * DUALMUL;
       heptagon *h2 = createStep(viewctr.at, i1);
       transmatrix T = (binarytiling) ? binary::relative_matrix(h2, viewctr.at) : arcm::relative_matrix(h2, viewctr.at);
       hyperpoint H = View * tC0(T);