diff --git a/conformal.cpp b/conformal.cpp
index e95cbd22..8cd00687 100644
--- a/conformal.cpp
+++ b/conformal.cpp
@@ -424,6 +424,8 @@ namespace conformal {
   
   cld spiral_multiplier;
   ld right_spiral_multiplier = 1;
+  ld any_spiral_multiplier = 1;
+  ld sphere_spiral_multiplier = 2;
   ld spiral_cone = 360;
   ld spiral_cone_rad;
   bool ring_not_spiral;
@@ -439,19 +441,18 @@ namespace conformal {
     model_straight_yz = DIM == 2 || (ocos_yz > 1-1e-9);
     if(conformal::on) conformal::apply();
     
-    if(hyperbolic) {
+    if(!euclid) {
       ld b = spiral_angle * degree;
       ld cos_spiral = cos(b);
       ld sin_spiral = sin(b);
       spiral_cone_rad = spiral_cone * degree;
       ring_not_spiral = abs(cos_spiral) < 1e-3;
-      if(ring_not_spiral) {
-        cos_spiral = 0;
-        sin_spiral = 1;
-        spiral_multiplier = cld(0, right_spiral_multiplier * spiral_cone_rad / 2);
-        }
-      else
-        spiral_multiplier = cld(cos_spiral, sin_spiral) * cld(spiral_cone_rad * cos_spiral / 2., 0);
+      ld mul = 1;
+      if(sphere) mul = .5 * sphere_spiral_multiplier;
+      else if(ring_not_spiral) mul = right_spiral_multiplier;
+      else mul = any_spiral_multiplier * cos_spiral;
+      
+      spiral_multiplier = cld(cos_spiral, sin_spiral) * cld(spiral_cone_rad * mul / 2., 0);
       }
     if(euclid) {
       hyperpoint h = tC0(eumove(spiral_x, spiral_y));
@@ -908,18 +909,28 @@ namespace conformal {
         });
       }
     
-    if(pmodel == mdSpiral && hyperbolic) {
+    if(pmodel == mdSpiral && !euclid) {
       dialog::addSelItem(XLAT("spiral angle"), fts(spiral_angle), 'x');
       dialog::add_action([](){
         dialog::editNumber(spiral_angle, 0, 360, 15, 0, XLAT("spiral angle"), "");
         });
 
-      if(ring_not_spiral) {
-        dialog::addSelItem(XLAT("spiral multiplier"), fts(right_spiral_multiplier), 'M');
-        dialog::add_action([](){
-          dialog::editNumber(right_spiral_multiplier, 0, 10, -.1, 1, XLAT("spiral multiplier"), "");
-          });
-        }
+      ld& which =
+        sphere ? sphere_spiral_multiplier :
+        ring_not_spiral ? right_spiral_multiplier :
+        any_spiral_multiplier;
+                
+      dialog::addSelItem(XLAT("spiral multiplier"), fts(which), 'M');
+      dialog::add_action([&which](){
+        dialog::editNumber(which, 0, 10, -.1, 1, XLAT("spiral multiplier"), 
+          XLAT(
+            "This parameter has a bit different scale depending on the settings:\n"
+            "(1) in spherical geometry (with spiral angle=90, 1 produces a stereographic projection)\n"
+            "(2) in hyperbolic geometry, with spiral angle being +90° or -90°\n"
+            "(3) in hyperbolic geometry, with other spiral angles (1 makes the bands fit exactly)"
+            )
+          );
+        });
 
       dialog::addSelItem(XLAT("spiral cone"), fts(spiral_cone), 'C');
       dialog::add_action([](){
@@ -1225,9 +1236,14 @@ namespace conformal {
     else if(argis("-sang")) { 
       PHASEFROM(2); 
       shift_arg_formula(conformal::spiral_angle);
-      if(conformal::spiral_angle == 90) {
+      if(sphere)
+        shift_arg_formula(conformal::sphere_spiral_multiplier);
+      else if(conformal::spiral_angle == 90)
         shift_arg_formula(conformal::right_spiral_multiplier);
-        }        
+      }
+    else if(argis("-ssm")) { 
+      PHASEFROM(2);
+      shift_arg_formula(conformal::any_spiral_multiplier);
       }
     else if(argis("-scone")) { 
       PHASEFROM(2); 
diff --git a/hypgraph.cpp b/hypgraph.cpp
index e25e9446..365c8523 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -192,11 +192,12 @@ template<class T> void makeband(hyperpoint H, hyperpoint& ret, const T& f) {
   
   ld x, y, yf, zf=0;
   y = asin_auto(H[1]);
-  x = asin_auto_clamp(H[0] / cos_auto(y)) + band_shift;
+  x = asin_auto_clamp(H[0] / cos_auto(y));
   if(sphere) {
     if(H[DIM] < 0 && x > 0) x = M_PI - x;
     else if(H[DIM] < 0 && x <= 0) x = -M_PI - x;
     }
+  x += band_shift;
   hypot_zlev(zlev, y, yf, zf);
   
   f(x, y);
@@ -628,7 +629,7 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
     
     case mdSpiral: {
       cld z;
-      if(hyperbolic) makeband(H, ret, band_conformal);
+      if(hyperbolic || sphere) makeband(H, ret, band_conformal);
       else ret = H;
       z = cld(ret[0], ret[1]) * conformal::spiral_multiplier;
       
@@ -910,7 +911,33 @@ void drawrec(cell *c, const transmatrix& V) {
 
 vector<tuple<heptspin, hstate, transmatrix, ld> > drawn_cells;
 
+bool in_multi = false;
+
 void hrmap_standard::draw() {
+  if(sphere && pmodel == mdSpiral && !in_multi) {
+    in_multi = true;
+    if(conformal::ring_not_spiral) {
+      int qty = ceil(1. / conformal::sphere_spiral_multiplier);
+      if(qty > 100) qty = 100;
+      for(int i=-qty; i < qty; i++) {
+        band_shift = 2 * M_PI * i;
+        draw();
+        }
+      }
+    else {
+      draw();
+      if(vid.use_smart_range) for(int i=1;; i++) {
+        int drawn = cells_drawn;
+        band_shift = 2 * M_PI * i;
+        draw();
+        band_shift = -2 * M_PI * i;
+        draw();
+        if(drawn == cells_drawn) break;
+        }
+      }
+    in_multi = false;
+    return;
+    }
   drawn_cells.clear();
   drawn_cells.emplace_back(viewctr, hsOrigin, cview(), band_shift);
   for(int i=0; i<isize(drawn_cells); i++) {    
@@ -972,6 +999,8 @@ void hrmap_standard::draw() {
           }
         }
       }
+    
+    if(sphere) draw = true;
   
     if(draw) for(int d=0; d<S7; d++) {
       hstate s2 = transition(s, d);
@@ -1556,6 +1585,7 @@ void draw_boundary(int w) {
     case mdSpiral: {
       using namespace hyperpoint_vec;
       if(euclid) return;
+      if(conformal::ring_not_spiral) return;
       // if(p == PPR::CIRCLE) p = PPR::OUTCIRCLE;
       auto& sm = conformal::spiral_multiplier;
       ld u = hypot(1, imag(sm) / real(sm));
@@ -1590,13 +1620,17 @@ void draw_boundary(int w) {
 
 ld band_shift = 0;
 void fix_the_band(transmatrix& T) {
-  if((models[pmodel].flags & mf::quasiband) && T[2][2] > 1e6) {
+  if(((models[pmodel].flags & mf::quasiband) && T[DIM][DIM] > 1e6) || (sphere && pmodel == mdSpiral)) {
     hyperpoint H = tC0(T);
     find_zlev(H);
     conformal::apply_orientation(H[0], H[1]);
     
     ld y = asin_auto(H[1]);
     ld x = asin_auto_clamp(H[0] / cos_auto(y));
+    if(sphere) {
+      if(H[DIM] < 0 && x > 0) x = M_PI - x;
+      else if(H[DIM] < 0 && x <= 0) x = -M_PI - x;
+      }
     band_shift += x;
     // printf("fixing with shift = %lf\n", x);
     T = xpush(-x) * T;
@@ -1663,7 +1697,7 @@ bool do_draw(cell *c, const transmatrix& T) {
     ld iz = imag(z) + 1.14279e-2; // make it never fall exactly on PI
     if(iz < -M_PI || iz >= M_PI) return false;
     }
-  if(hyperbolic && pmodel == mdSpiral && conformal::ring_not_spiral) {
+  if(pmodel == mdSpiral && conformal::ring_not_spiral) {
     cld z;
     hyperpoint H = tC0(T);
     hyperpoint ret;