diff --git a/3d-models.cpp b/3d-models.cpp
index 8b60782a..aa721011 100644
--- a/3d-models.cpp
+++ b/3d-models.cpp
@@ -30,10 +30,15 @@ vector<hyperpoint> geometry_information::get_shape(hpcshape sh) {
   return res;  
   }
 
+hyperpoint normalize_flat(hyperpoint h) {
+  if(prod) return product_decompose(h).second;
+  return normalize(h);
+  }
+
 hyperpoint get_center(const vector<hyperpoint>& vh) {
   hyperpoint h = Hypc;
   for(auto h1: vh) h = h + h1;
-  return normalize(h);
+  return normalize_flat(h);
   }
 
 ld zc(ld z) { 
@@ -125,7 +130,7 @@ void geometry_information::add_texture(hpcshape& sh) {
 
 vector<hyperpoint> scaleshape(const vector<hyperpoint>& vh, ld s) {
   vector<hyperpoint> res;
-  for(hyperpoint h: vh) res.push_back(normalize(h * s + shcenter * (1-s)));
+  for(hyperpoint h: vh) res.push_back(normalize_flat(h * s + shcenter * (1-s)));
   return res;
   }
 
@@ -326,8 +331,8 @@ void geometry_information::make_armor_3d(hpcshape& sh, int kind) {
   
   for(hyperpoint h: body) {
     array<ld, 2> p;
-    p[0] = h[0] / h[3];
-    p[1] = h[1] / h[3];
+    p[0] = h[0] / h[LDIM];
+    p[1] = h[1] / h[LDIM];
     pts[0].emplace_back(p);
     }
   
@@ -394,8 +399,8 @@ void geometry_information::make_head_3d(hpcshape& sh) {
   
   for(hyperpoint h: head) {
     array<ld, 2> p;
-    p[0] = h[0] / h[3];
-    p[1] = h[1] / h[3];
+    p[0] = h[0] / h[LDIM];
+    p[1] = h[1] / h[LDIM];
     pts[0].emplace_back(p);
     }
   
@@ -476,6 +481,11 @@ void geometry_information::make_skeletal(hpcshape& sh, ld push) {
   shift_last(-push);
   }
 
+hyperpoint yzspin(ld alpha, hyperpoint h) {
+  if(prod) return product::direct_exp(cspin(1, 2, alpha) * product::inverse_exp(h));
+  else return cspin(1, 2, alpha) * h;
+  }
+
 void geometry_information::make_revolution(hpcshape& sh, int mx, ld push) {
   auto body = get_shape(sh);
   bshape(sh, PPR::MONSTER_BODY);
@@ -484,12 +494,12 @@ void geometry_information::make_revolution(hpcshape& sh, int mx, ld push) {
     hyperpoint h0 = body[i];
     hyperpoint h1 = body[(i+1) % isize(body)];
     for(int s=0; s<mx; s+=step) {
-      hpcpush(cspin(1, 2, s * degree) * h0);
-      hpcpush(cspin(1, 2, s * degree) * h1);
-      hpcpush(cspin(1, 2, (s+step) * degree) * h0);
-      hpcpush(cspin(1, 2, s * degree) * h1);
-      hpcpush(cspin(1, 2, (s+step) * degree) * h0);
-      hpcpush(cspin(1, 2, (s+step) * degree) * h1);
+      hpcpush(yzspin(s * degree, h0));
+      hpcpush(yzspin(s * degree, h1));
+      hpcpush(yzspin((s+step) * degree, h0));
+      hpcpush(yzspin(s * degree, h1));
+      hpcpush(yzspin((s+step) * degree, h0));
+      hpcpush(yzspin((s+step) * degree, h1));
       }
     }
   last->flags |= POLY_TRIANGLES;
@@ -537,7 +547,7 @@ void geometry_information::make_revolution_cut(hpcshape &sh, int each, ld push,
   for(int i=0; i<n; i++) if(!stillin[i] && !stillin[lastid[i]]) lastid[i] = lastid[lastid[i]];
 
   for(int i=0; i<n; i++) {
-    if(!stillin[i]) gbody[i] = normalize(gbody[lastid[i]] * (i - lastid[i]) + gbody[nextid[i]] * (nextid[i] - i));
+    if(!stillin[i]) gbody[i] = normalize_flat(gbody[lastid[i]] * (i - lastid[i]) + gbody[nextid[i]] * (nextid[i] - i));
     }
   
   bshape(sh, PPR::MONSTER_BODY);
@@ -551,12 +561,12 @@ void geometry_information::make_revolution_cut(hpcshape &sh, int each, ld push,
       hyperpoint h1 = tbody[i1];
       hyperpoint hs0 = nbody[i];
       hyperpoint hs1 = nbody[i1];
-      hpcpush(cspin(1, 2, s * degree) * h0);
-      hpcpush(cspin(1, 2, s * degree) * h1);
-      hpcpush(cspin(1, 2, (s+step) * degree) * hs0);
-      hpcpush(cspin(1, 2, s * degree) * h1);
-      hpcpush(cspin(1, 2, (s+step) * degree) * hs0);
-      hpcpush(cspin(1, 2, (s+step) * degree) * hs1);
+      hpcpush(yzspin(s * degree, h0));
+      hpcpush(yzspin(s * degree, h1));
+      hpcpush(yzspin((s+step) * degree, hs0));
+      hpcpush(yzspin(s * degree, h1));
+      hpcpush(yzspin((s+step) * degree, hs0));
+      hpcpush(yzspin((s+step) * degree, hs1));
       }
     }
   last->flags |= POLY_TRIANGLES;
@@ -600,26 +610,40 @@ void geometry_information::animate_bird(hpcshape& orig, hpcshape_animated& anima
   // shift_shape(orig, BIRD);
   }
 
+EX hyperpoint forward_dir(ld x) { return prod ? point3(x, 0, 0) : xpush0(x); }
+
+EX hyperpoint dir_to_point(hyperpoint h) { return prod ? product::direct_exp(h) : h; }
+
+EX hyperpoint dir_setlength(hyperpoint dir, ld length) {
+  if(dir[0] == 0 && dir[1] == 0 && dir[2] == 0) return dir;
+  if(prod) return dir * (length / hypot_d(3, dir));
+  return rspintox(dir) * xpush0(length);
+  }
+
 void geometry_information::slimetriangle(hyperpoint a, hyperpoint b, hyperpoint c, ld rad, int lev) {
   dynamicval<int> d(vid.texture_step, 8);
   texture_order([&] (ld x, ld y) {
     ld z = 1-x-y;
-    ld r = scalefactor * hcrossf7 * (0 + pow(max(x,max(y,z)), .3) * 0.8);
-    hyperpoint h = rspintox(a*x+b*y+c*z) * xpush0(r);
+    ld r = scalefactor * hcrossf7 * (0 + pow(max(x,max(y,z)), .3) * 0.8) * (prod ? .5 : 1);
+    hyperpoint h = dir_to_point(dir_setlength(a*x+b*y+c*z, r));
     hpcpush(h);
     });  
   }
 
 void geometry_information::balltriangle(hyperpoint a, hyperpoint b, hyperpoint c, ld rad, int lev) {
   if(lev == 0) {
-    hpcpush(a);
-    hpcpush(b);
-    hpcpush(c);
+    hpcpush(dir_to_point(a));
+    hpcpush(dir_to_point(b));
+    hpcpush(dir_to_point(c));
     }
   else {
-    hyperpoint cx = rspintox(mid(a,b)) * xpush0(rad);
-    hyperpoint ax = rspintox(mid(b,c)) * xpush0(rad);
-    hyperpoint bx = rspintox(mid(c,a)) * xpush0(rad);
+    auto midpoint = [&] (hyperpoint h1, hyperpoint h2) {
+      if(prod) return dir_setlength(h1+h2, rad);
+      else return rspintox(mid(h1,h2)) * xpush0(rad);
+      };
+    hyperpoint cx = midpoint(a, b);
+    hyperpoint ax = midpoint(b, c);
+    hyperpoint bx = midpoint(c, a);
     balltriangle(ax, bx, cx, rad, lev-1);
     balltriangle(ax, bx, c , rad, lev-1);
     balltriangle(ax, b , cx, rad, lev-1);
@@ -630,8 +654,8 @@ void geometry_information::balltriangle(hyperpoint a, hyperpoint b, hyperpoint c
 void geometry_information::make_ball(hpcshape& sh, ld rad, int lev) {
   bshape(sh, sh.prio);
   sh.flags |= POLY_TRIANGLES;
-  hyperpoint tip = xpush0(rad);
-  hyperpoint atip = xpush0(-rad);
+  hyperpoint tip = forward_dir(rad);
+  hyperpoint atip = forward_dir(-rad);
   ld z = 63.43 * degree;
   for(int i=0; i<5; i++) {
     hyperpoint a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * tip;
@@ -691,7 +715,13 @@ void geometry_information::make_euclidean_sky() {
       );
   }
 
+/** res[0] and res[1] place H on the plane, while res[2] is the altitude */
 hyperpoint psmin(hyperpoint H) {
+  if(prod) {
+    auto d = product_decompose(H);
+    d.second[2] = d.first;
+    return d.second;
+    }
   hyperpoint res;
   res[2] = asin_auto(H[2]);
   ld cs = pow(cos_auto(res[2]), 2);
@@ -704,7 +734,7 @@ hyperpoint psmin(hyperpoint H) {
 void geometry_information::adjust_eye(hpcshape& eye, hpcshape head, ld shift_eye, ld shift_head, int q, ld zoom) {
   hyperpoint center = Hypc;
   for(int i=eye.s; i<eye.e; i++) if(q == 1 || hpc[i][1] > 0) center += hpc[i];
-  center = normalize(center);
+  center = normalize_flat(center);
   // center /= (eye.e - eye.s);
   ld rad = 0;
   for(int i=eye.s; i<eye.e; i++) if(q == 1 || hpc[i][1] > 0) rad += hdist(center, hpc[i]);
@@ -724,7 +754,7 @@ void geometry_information::adjust_eye(hpcshape& eye, hpcshape head, ld shift_eye
   zmid /= isize(pss);
   
   ld mindist = 1e9;
-  for(int i=0; i<isize(pss); i+=3) if(pss[i][2] < zmid || WDIM == 3) {
+  for(int i=0; i<isize(pss); i+=3) if(prod ? pss[i][2] > zmid : (pss[i][2] < zmid || (WDIM == 3 && !prod))) {
     ld d = sqhypot_d(2, pss[i]-pscenter) + sqhypot_d(2, pss[i+1]-pscenter) + sqhypot_d(2, pss[i+2]-pscenter);
     if(d < mindist) mindist = d, pos = min(min(pss[i][2], pss[i+1][2]), pss[i+2][2]), qty++;
     qtyall++;
@@ -1086,10 +1116,10 @@ void geometry_information::make_3d_models() {
   hyperpoint atip = xpush0(-1);
   ld z = 63.43 * degree;
   for(int i=0; i<5; i++) {
-    auto a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * xpush0(1);
-    auto b = cspin(1, 2, (72 * i-72) * degree) * spin(z) * xpush0(1);
-    auto c = cspin(1, 2, (72 * i+36) * degree) * spin(M_PI-z) * xpush0(1);
-    auto d = cspin(1, 2, (72 * i-36) * degree) * spin(M_PI-z) * xpush0(1);
+    auto a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * forward_dir(1);
+    auto b = cspin(1, 2, (72 * i-72) * degree) * spin(z) * forward_dir(1);
+    auto c = cspin(1, 2, (72 * i+36) * degree) * spin(M_PI-z) * forward_dir(1);
+    auto d = cspin(1, 2, (72 * i-36) * degree) * spin(M_PI-z) * forward_dir(1);
     slimetriangle(tip, a, b, 1, 0);
     slimetriangle(a, b, c, 1, 0);
     slimetriangle(b, c, d, 1, 0);
diff --git a/control.cpp b/control.cpp
index 2b1cdc03..3bbdd7a9 100644
--- a/control.cpp
+++ b/control.cpp
@@ -113,7 +113,7 @@ EX void remission() {
  }
 
 EX hyperpoint move_destination_vec(int d) {
-  hyperpoint Forward = prod ? hpxy3(1,0,0) : tC0(pushone());
+  hyperpoint Forward = prod ? forward_dir(1) : tC0(pushone());
   if(WDIM == 2) return spin(-d * M_PI/4) * tC0(pushone());
   // else if(WDIM == 2 && pmodel == mdPerspective) return cspin(0, 2, d * M_PI/4) * tC0(pushone());
   // else if(WDIM == 2) return spin(-d * M_PI/4) * tC0(pushone());
diff --git a/geometry.cpp b/geometry.cpp
index 9e1c4e89..65e660c9 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -437,6 +437,20 @@ void geometry_information::prepare_basics() {
     goto finish;
     }
   
+  if(prod) {
+    auto t = this;
+    product::in_underlying_geometry([&] {
+      t->rhexf = cgi.rhexf;
+      t->hexf = cgi.hexf;
+      t->crossf = cgi.crossf;
+      t->hcrossf = cgi.crossf;
+      t->tessf = cgi.tessf;
+      t->hexhexdist = cgi.hexhexdist;
+      t->base_distlimit = cgi.base_distlimit-1;
+      });
+    goto prod_finish;
+    }
+  
   if((sphere || hyperbolic) && WDIM == 3 && !binarytiling) {
     rhexf = hexf = 0.378077;
     crossf = hcrossf = 0.620672;
@@ -512,6 +526,8 @@ void geometry_information::prepare_basics() {
   if(binarytiling) binary::build_tmatrix();
   #endif
   
+  prod_finish:
+  
   scalefactor = crossf / hcrossf7;
   orbsize = crossf;
 
diff --git a/graph.cpp b/graph.cpp
index 6b8e54d4..0f68c178 100644
--- a/graph.cpp
+++ b/graph.cpp
@@ -1345,7 +1345,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const transmatrix& V1, color_t
   char xch = minf[m].glyph;
   
   transmatrix V = V1;
-  if(WDIM == 3 && (classflag(m) & CF_FACE_UP) && where) V = V1 * cspin(0, 2, M_PI/2);
+  if(WDIM == 3 && (classflag(m) & CF_FACE_UP) && where && !prod) V = V1 * cspin(0, 2, M_PI/2);
 
   // if(GDIM == 3) V = V * cspin(0, 2, M_PI/2);
 
@@ -2749,7 +2749,7 @@ bool drawMonster(const transmatrix& Vparam, int ct, cell *c, color_t col, bool m
   else {
     // other monsters face the player
     
-    if(!nospins) {
+    if(!nospins && !prod) {
       if(WDIM == 2) {
         hyperpoint V0 = inverse(cwtV) * tC0(Vs);
         hyperpoint V1 = spintox(V0) * V0;
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index 9fc3badc..b2990eaf 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -132,8 +132,8 @@ const static transmatrix pispin = diag(-1,-1,1,1);
 // central symmetry
 const static transmatrix centralsym = diag(-1,-1,-1,-1);
 
-inline hyperpoint hpxyz(ld x, ld y, ld z) { return GDIM == 2 ? hyperpoint(x,y,z,0) : hyperpoint(x,y,0,z); }
-inline hyperpoint hpxyz3(ld x, ld y, ld z, ld w) { return GDIM == 2 ? hyperpoint(x,y,w,0) : hyperpoint(x,y,z,w); }
+inline hyperpoint hpxyz(ld x, ld y, ld z) { return MDIM == 3 ? hyperpoint(x,y,z,0) : hyperpoint(x,y,0,z); }
+inline hyperpoint hpxyz3(ld x, ld y, ld z, ld w) { return MDIM == 3 ? hyperpoint(x,y,w,0) : hyperpoint(x,y,z,w); }
 inline hyperpoint point3(ld x, ld y, ld z) { return hyperpoint(x,y,z,0); }
 inline hyperpoint point31(ld x, ld y, ld z) { return hyperpoint(x,y,z,1); }
 inline hyperpoint point2(ld x, ld y) { return hyperpoint(x,y,0,0); }
@@ -450,7 +450,7 @@ EX transmatrix euaffine(hyperpoint h) {
 EX transmatrix cpush(int cid, ld alpha) {
   transmatrix T = Id;
   if(prod && cid == 2)
-    return mscale(Id, exp(alpha));
+    return mscale(Id, alpha);
   if(nonisotropic) 
     return eupush3(cid == 0 ? alpha : 0, cid == 1 ? alpha : 0, cid == 2 ? alpha : 0);
   T[LDIM][LDIM] = T[cid][cid] = cos_auto(alpha);
@@ -473,6 +473,7 @@ EX bool eqmatrix(transmatrix A, transmatrix B, ld eps IS(.01)) {
 #if MAXMDIM >= 4
 // in the 3D space, move the point h orthogonally to the (x,y) plane by z units
 EX hyperpoint orthogonal_move(const hyperpoint& h, ld z) {
+  if(prod) return zshift(h, z);
   if(!hyperbolic) return rgpushxto0(h) * cpush(2, z) * C0;
   if(nil) return nisot::translate(h) * cpush0(2, z);
   if(translatable) return hpxy3(h[0], h[1], h[2] + z);
@@ -622,7 +623,7 @@ EX transmatrix ggpushxto0(const hyperpoint& H, ld co) {
     }
   if(prod) {
     auto d = product_decompose(H);
-    return mscale(PIU(ggpushxto0(d.second, co)), exp(d.first * co));
+    return mscale(PIU(ggpushxto0(d.second, co)), d.first * co);
     }
   transmatrix res = Id;
   if(sqhypot_d(GDIM, H) < 1e-12) return res;
@@ -764,7 +765,7 @@ EX transmatrix inverse(const transmatrix& T) {
 
 EX pair<ld, hyperpoint> product_decompose(hyperpoint h) {
   ld z = zlevel(h);
-  return make_pair(z, mscale(h, exp(-z)));
+  return make_pair(z, mscale(h, -z));
   }
 
 // distance between mh and 0
@@ -829,6 +830,7 @@ EX ld hdist(const hyperpoint& h1, const hyperpoint& h2) {
 
 EX hyperpoint mscale(const hyperpoint& t, double fac) {
   if(GDIM == 3 && !prod) return cpush(2, fac) * t;
+  if(prod) fac = exp(fac);
   hyperpoint res;
   for(int i=0; i<MDIM; i++) 
     res[i] = t[i] * fac;
@@ -840,6 +842,7 @@ EX transmatrix mscale(const transmatrix& t, double fac) {
     // if(pmodel == mdFlatten) { transmatrix u = t; u[2][LDIM] -= fac; return u; }
     return t * cpush(2, fac);
     }
+  if(prod) fac = exp(fac);
   transmatrix res;
   for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
     res[i][j] = t[i][j] * fac;
@@ -912,7 +915,7 @@ EX hyperpoint orthogonal_of_C0(hyperpoint h0, hyperpoint h1, hyperpoint h2) {
 
 EX hyperpoint zshift(hyperpoint x, ld z) {
   if(GDIM == 3 && WDIM == 2) return rgpushxto0(x) * cpush0(2, z);
-  else if(prod) return mscale(x, exp(z));
+  else if(prod) return mscale(x, z);
   else return mscale(x, z);
   }
 
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 8742da0d..5d03011f 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -1353,7 +1353,7 @@ EX void centerpc(ld aspd) {
       auto d = product_decompose(H);
       ld dist = -d.first / R * aspd;
       if(abs(dist) > abs(d.first)) dist = -d.first;
-      View = mscale(View, exp(dist));
+      View = mscale(View, dist);
       aspd *= sqrt(R*R - d.first * d.first) / R;
       }
 
@@ -1377,9 +1377,11 @@ EX void optimizeview() {
   
   if(prod) {
     ld z = zlevel(tC0(View));
-    View = mscale(View, exp(-z));
+    View = mscale(View, -z);
     product::in_underlying_geometry(optimizeview);
-    View = mscale(View, exp(z));
+    if(z > product::plevel / 2) { product::current_view_level--; z -= product::plevel; }
+    if(z < -product::plevel / 2) { product::current_view_level++; z += product::plevel; }
+    View = mscale(View, z);
     return;
     }
   
@@ -1473,6 +1475,7 @@ EX void resetview() {
   else centerover = cwt;
   cwtV = View;
   nisot::local_perspective = Id;
+  if(prod) product::current_view_level = product::get_where(cwt.at).second;
   // SDL_LockSurface(s);
   // SDL_UnlockSurface(s);
   }
diff --git a/nonisotropic.cpp b/nonisotropic.cpp
index bd934689..d3cc7742 100644
--- a/nonisotropic.cpp
+++ b/nonisotropic.cpp
@@ -553,7 +553,6 @@ EX namespace product {
     underlying_cgip = cgip;
     geometry = gProduct;
     ginf[gProduct] = ginf[underlying];
-    ginf[gProduct].sides += 2;
     ginf[gProduct].cclass = gcProduct;
     ginf[gProduct].flags |= qEXPERIMENTAL;
     pmodel = mdPerspective;
@@ -561,6 +560,8 @@ EX namespace product {
   
   EX ld plevel = 1;
   
+  EX int current_view_level;
+  
   hrmap *pmap;
   geometry_information *pcgip;
   
@@ -599,7 +600,7 @@ EX namespace product {
     cell* gamestart() override { return getCell(underlying_map->gamestart(), 0); }
   
     transmatrix relative_matrix(cell *c2, cell *c1, const hyperpoint& point_hint) override {
-      return in_underlying([&] { return calc_relative_matrix(where[c2].first, where[c1].first, point_hint); }) * mscale(Id, exp(plevel * (where[c2].second - where[c1].second)));
+      return in_underlying([&] { return calc_relative_matrix(where[c2].first, where[c1].first, point_hint); }) * mscale(Id, plevel * (where[c2].second - where[c1].second));
       }
   
     hrmap_product() {
@@ -611,12 +612,14 @@ EX namespace product {
       }
     };
   
-  cell *get_at(cell *base, int level) {
+  EX cell *get_at(cell *base, int level) {
     return ((hrmap_product*)currentmap)->getCell(base, level);
     }
   
+  EX pair<cell*, int> get_where(cell *c) { return ((hrmap_product*)currentmap)->where[c]; }
+  
   void drawcell_stack(cell *c, transmatrix V, int spinv, bool mirrored) {
-    in_actual([&] { for(int z=-5; z<=5; z++) drawcell(get_at(c, z), V * mscale(Id, exp(plevel * z)), spinv, mirrored); });
+    in_actual([&] { for(int z=-5; z<=5; z++) drawcell(get_at(c, current_view_level+z), V * mscale(Id, plevel * z), spinv, mirrored); });
     }
   
   void find_cell_connection(cell *c, int d) {
diff --git a/polygons.cpp b/polygons.cpp
index 700f09c9..9ee225eb 100644
--- a/polygons.cpp
+++ b/polygons.cpp
@@ -755,7 +755,7 @@ vector<hyperpoint> make5(hyperpoint a, hyperpoint b, hyperpoint c) {
 
 void geometry_information::create_wall3d() {
   if(WDIM == 2) return;
-  int howmany = penrose ? 22 : S7;
+  int howmany = penrose ? 22 : prod ? S7+2 : S7;
   shWall3D.resize(howmany);
   shPlainWall3D.resize(howmany);
   shWireframe3D.resize(howmany);
@@ -857,15 +857,15 @@ void geometry_information::create_wall3d() {
   
   if(prod) {
     cell model;
-    model.type = S7-2;
-    for(int i=0; i<S7-2; i++)
+    model.type = S7;
+    for(int i=0; i<S7; i++)
       make_wall(i, {product::get_corner(&model, i, -1), product::get_corner(&model, i, +1), product::get_corner(&model, i+1, +1), product::get_corner(&model, i+1, -1)});
     for(int a: {0,1}) {
       vector<hyperpoint> l;
       int z = a ? 1 : -1;
-      for(int i=0; i<S7-2; i++)
+      for(int i=0; i<S7; i++)
         l.push_back(product::get_corner(&model, i, z));
-      make_wall(S7-2+a, l);
+      make_wall(S7+a, l);
       }    
     }