diff --git a/classes.cpp b/classes.cpp
index a9aa0a86..2ab79d53 100644
--- a/classes.cpp
+++ b/classes.cpp
@@ -723,7 +723,7 @@ enum eGeometry {
   gKiteDart2, gKiteDart3, gNil, gProduct, gRotSpace,
   gTernary, gNIH, gSolN, gInfOrder, gSpace336, gSpace344, gCrystal344,
   gArnoldCat, gArbitrary, gInfOrder4, gCrystal534,
-  gSpace535, gSpace536, gSeifertCover,
+  gSpace535, gSpace536, gSeifertCover, gSeifertWeber, gHomologySphere,
   gGUARD};
 
 enum eGeometryClass { gcHyperbolic, gcEuclid, gcSphere, gcSolNIH, gcNil, gcProduct, gcSL2 };
@@ -785,6 +785,7 @@ static const flagtype qNIH             = 65536;
 static const flagtype qIDEAL           = 131072;
 static const flagtype qHUGE_BOUNDED    = 262144;
 static const flagtype qOPTQ            = Flag(19);
+static const flagtype qSINGLE          = Flag(20);
 
 // note: dnext assumes that x&7 equals 7
 static const int SEE_ALL = 50;
@@ -807,6 +808,8 @@ static const flagtype qsSMALLBF         = qsSMALLB | qsFIELD | qANYQ;
 static const flagtype qsSMALLBE         = qsSMALLB | qELLIPTIC | qANYQ;
 static const flagtype qsBP              = qBINARY | qKITE;
 
+static const flagtype qsSINGLE          = qANYQ | qSMALL | qBOUNDED | qSINGLE;
+
 EX geometryinfo1 giEuclid2 = { gcEuclid,     2, 2, 3, {1,1, 0,0 } };
 EX geometryinfo1 giHyperb2 = { gcHyperbolic, 2, 2, 3, {1,1,-1,0 } };
 EX geometryinfo1 giSphere2 = { gcSphere,     2, 2, 3, {1,1,+1,0 } };
@@ -893,6 +896,8 @@ EX vector<geometryinfo> ginf = {
   {"{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},
   {"{5,3,5}","SWh",     "{5,3,5} quotient",                           "535c",    12, 5, qsSMALLB | qANYQ, giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
+  {"{5,3,5}","SW",      "Seifert-Weber space",                        "535s",    12, 5, qsSINGLE,  giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
+  {"{5,3,3}","SW",      "Poincaré homology sphere",                   "533s",    12, 3, qsSINGLE,  giSphere3, 0x31400, {{7, 2}}, eVariation::pure},
   };
   // bits: 9, 10, 15, 16, (reserved for later) 17, 18
 
diff --git a/reg3.cpp b/reg3.cpp
index d1328a25..0a8159ed 100644
--- a/reg3.cpp
+++ b/reg3.cpp
@@ -687,6 +687,20 @@ EX namespace reg3 {
       return res;
       }
 
+    struct hrmap_singlecell : hrmap_quotient3 {    
+      hrmap_singlecell(ld angle) {
+        generate();
+        initialize(1);
+        tmatrices[0].resize(S7);
+        for(int b=0; b<S7; b++) {
+          allh[0]->c.connect(b, allh[0], (b+S7/2) % S7, false);
+          transmatrix T = reg3::adjmoves[b];
+          hyperpoint p = tC0(T);
+          tmatrices[0][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, angle) * spintox(p);
+          }
+        }
+      };
+
     struct hrmap_seifert_cover : hrmap_quotient3 {
 
       hrmap_seifert_cover() {
@@ -1014,6 +1028,8 @@ EX namespace reg3 {
   
 EX hrmap* new_map() {
   if(geometry == gSeifertCover) return new seifert_weber::hrmap_seifert_cover;
+  if(geometry == gSeifertWeber) return new seifert_weber::hrmap_singlecell(108*degree);
+  if(geometry == gHomologySphere) return new seifert_weber::hrmap_singlecell(36*degree);
   if(quotient && !sphere) return new hrmap_field3;
   return new hrmap_reg3;
   }
@@ -1039,6 +1055,7 @@ EX int celldistance(cell *c1, cell *c2) {
 
 EX bool pseudohept(cell *c) {
   auto m = regmap();
+  if(cgflags & qSINGLE) return true;
   if(sphere) {
     hyperpoint h = tC0(m->relative_matrix(c->master, regmap()->origin, C0));
     if(S7 == 12) {