diff --git a/drawing.cpp b/drawing.cpp
index e9b13163..7774c497 100644
--- a/drawing.cpp
+++ b/drawing.cpp
@@ -353,7 +353,8 @@ EX int get_side(const hyperpoint& H) {
   if(pmodel == mdRotatedHyperboles)
     return H[1] > 0 ? -1 : 1;
   if(pmodel == mdHyperboloid) {
-    return det2(pconf.ball() * cspin90(2, 1) * rgpushxto0(H)) > 0 ? 1 : -1;
+    auto H1 = H; if(sphere && pconf.small_hyperboloid) H1 = mid(H, C0);
+    return det2(pconf.ball() * cspin90(2, 1) * rgpushxto0(H1)) > 0 ? 1 : -1;
     }
   if(pmodel == mdHyperboloidFlat && sphere)
     return H[2] >= 0 ? 1 : -1;
@@ -364,6 +365,7 @@ EX int get_side(const hyperpoint& H) {
     }
   if(pmodel == mdHemisphere && sphere) {
     auto H1 = H;
+    if(pconf.small_hyperboloid) H1 = mid(H, C0);
     int s = H1[2] > 0 ? 1 : -1;
     if(hemi_side && s != hemi_side) return -spherespecial;
     H1[0] /= H1[2]; H1[1] /= H1[2];
@@ -570,6 +572,16 @@ void addpoly(const shiftmatrix& V, const vector<glvertex> &tab, int ofs, int cnt
     
     for(auto& p: tofix)
       fixpoint(glcoords[p.first], p.second);
+
+    if(sphere && among(pmodel, mdHemisphere, mdHyperboloid) && pconf.small_hyperboloid) {
+      bool left = false, right = false;
+      for(auto h: glcoords) { hyperpoint h1; applymodel(shiftless(glhr::gltopoint(h)), h1);
+        if(h1[0] < -0) left = true;
+        if(h1[0] > +0) right = true;
+        }
+      if(left && right) poly_flags |= POLY_NIF_ERROR;
+      }
+
     /*
     hyperpoint Hscr;
     applymodel(goodpoint, Hscr); 
@@ -2016,6 +2028,8 @@ void dqi_poly::draw() {
   if(pmodel == mdDisk && hyperbolic && pconf.alpha <= -1) can_have_inverse = true;
   if(pmodel == mdSpiral && pconf.skiprope) can_have_inverse = true;
   if(pmodel == mdCentralInversion) can_have_inverse = true;
+
+  if(among(pmodel, mdHemisphere, mdHyperboloid) && sphere && pconf.small_hyperboloid) can_have_inverse = true;
     
   if(can_have_inverse && !(poly_flags & POLY_ISSIDE)) {
   
@@ -2035,6 +2049,8 @@ void dqi_poly::draw() {
     
     }
   else poly_flags &=~ POLY_INVERSE;
+
+  if(among(pmodel, mdHemisphere, mdHyperboloid) && sphere && pconf.small_hyperboloid && (poly_flags & POLY_INVERSE)) return;
   
   if(spherespecial) {
     if(!(poly_flags & POLY_INFRONT)) return;
@@ -2433,7 +2449,7 @@ EX void draw_main() {
     return;
     }
 
-  if(pmodel == mdHemisphere && sphere && hemi_side == 0 && !vrhr::rendering()) {
+  if(pmodel == mdHemisphere && sphere && hemi_side == 0 && !vrhr::rendering() && !pconf.small_hyperboloid) {
     hemi_side = (pconf.ball() * hyperpoint(0,1,0,1)) [2] < 0 ? 1 : -1;
     draw_main();
 
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 855e18af..7032c7df 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -925,6 +925,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
 
       switch(cgclass) {
         case gcHyperbolic: {
+          if(pconf.small_hyperboloid) H = mid(C0, H);
           ld zl = zlevel(H);
           ret = H / H[2];
           ret[2] = sqrt(1 - sqhypot_d(2, ret));
@@ -944,11 +945,13 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
             ret[2] = (1 - y);
             ret[2] *= dir;
             ret = ret * (1 + (H[2]-1) * y * pconf.depth_scaling * dir / pconf.euclid_to_sphere);
+            if(pconf.small_hyperboloid) { ret = ret - C0; ret = ret / hypot_d(3, ret); }
             }
           break;
           }
         
         case gcSphere: {
+          if(pconf.small_hyperboloid) H = mid(C0, H);
           if(vrhr::rendering()) { vr_sphere(ret, H, md); return; }
           ld z = sqhypot_d(3, H);
           int s = H[2] > 0 ? 1 : -1;
diff --git a/models.cpp b/models.cpp
index bc3a2aea..73067c2a 100644
--- a/models.cpp
+++ b/models.cpp
@@ -425,6 +425,7 @@ EX namespace models {
     USING_NATIVE_GEOMETRY_IN_RUG;
     #endif
     dialog::init(XLAT("models & projections"));
+    mouseovers = XLAT("see http://www.roguetemple.com/z/hyper/models.php");
     
     auto vpmodel = vpconf.model;
     
@@ -626,10 +627,11 @@ EX namespace models {
       add_edit(vpconf.fisheye_alpha);
       }
 
-    if(is_hyperboloid(vpmodel)) {
+    if(is_hyperboloid(vpmodel))
       add_edit(pconf.show_hyperboloid_flat);
+
+    if(among(vpmodel, mdHyperboloid, mdHemisphere))
       add_edit(pconf.small_hyperboloid);
-      }
     
     if(vpmodel == mdCollignon) 
       add_edit(vpconf.collignon_parameter);
@@ -1045,8 +1047,8 @@ EX namespace models {
       -> editable("show flat", 'b');
   
       param_b(p.small_hyperboloid, sp+"hyperboloid-small", false)
-      -> editable("small hyperboloid model", 't')
-      -> help("as in Clifford algebras");
+      -> editable("halve distances", 'h')
+      -> help("This option halves the distances of every point from the center. Useful in the Minkowski hyperboloid model, to get a visualization of an alternative hyperboloid model based on Clifford algebras.");
 
       param_f(p.skiprope, sp+"mobius", 0)
       -> editable(0, 360, 15, "Möbius transformations", "", 'S')->unit = "°";