diff --git a/cell.cpp b/cell.cpp
index 475ac646..8405fb16 100644
--- a/cell.cpp
+++ b/cell.cpp
@@ -606,15 +606,34 @@ cell*& euclideanAt(eucoord x, eucoord y) {
 cell*& euclideanAtCreate(eucoord x, eucoord y) {
   cell*& c = euclideanAt(x,y);
   if(!c) {
-    c = newCell(6, NULL);
+    c = newCell(a4 ? (nontruncated || ((x^y^1) & 1) ? 4 : 8) : 6, NULL);
     c->master = encodeMaster(x,y);
     euclideanAt(x,y) = c;
-    eumerge(c, euclideanAt(x+1,y), 0, 3);
-    eumerge(c, euclideanAt(x,y+1), 1, 4);
-    eumerge(c, euclideanAt(x-1,y+1), 2, 5);
-    eumerge(c, euclideanAt(x-1,y), 3, 0);
-    eumerge(c, euclideanAt(x,y-1), 4, 1);
-    eumerge(c, euclideanAt(x+1,y-1), 5, 2);
+    if(c->type == 4) {
+      int m = nontruncated ? 1 : 2;
+      eumerge(c, euclideanAt(x+1,y), 0, 2 * m);        
+      eumerge(c, euclideanAt(x,y+1), 1, 3 * m);
+      eumerge(c, euclideanAt(x-1,y), 2, 0 * m);
+      eumerge(c, euclideanAt(x,y-1), 3, 1 * m);
+      }
+    else if(c->type == 8) {
+      eumerge(c, euclideanAt(x+1,y), 0, 2);
+      eumerge(c, euclideanAt(x+1,y+1), 1, 5);
+      eumerge(c, euclideanAt(x,y+1), 2, 3);
+      eumerge(c, euclideanAt(x-1,y+1), 3, 7);
+      eumerge(c, euclideanAt(x-1,y), 4, 0);
+      eumerge(c, euclideanAt(x-1,y-1), 5, 1);
+      eumerge(c, euclideanAt(x,y-1), 6, 1);
+      eumerge(c, euclideanAt(x+1,y-1), 7, 3);
+      }
+    else /* 6 */ {
+      eumerge(c, euclideanAt(x+1,y), 0, 3);
+      eumerge(c, euclideanAt(x,y+1), 1, 4);
+      eumerge(c, euclideanAt(x-1,y+1), 2, 5);
+      eumerge(c, euclideanAt(x-1,y), 3, 0);
+      eumerge(c, euclideanAt(x,y-1), 4, 1);
+      eumerge(c, euclideanAt(x+1,y-1), 5, 2);
+      }
     }
   return c;
   }
@@ -719,6 +738,7 @@ void verifycells(heptagon *at) {
 int eudist(short sx, short sy) {
   int z0 = abs(sx);
   int z1 = abs(sy);
+  if(a4) return z0 + z1;
   int z2 = abs(sx+sy);
   return max(max(z0,z1), z2);
   }
diff --git a/classes.cpp b/classes.cpp
index faeeaca5..e68bdee0 100644
--- a/classes.cpp
+++ b/classes.cpp
@@ -1620,5 +1620,6 @@ geometryinfo ginf[gGUARD] = {
   {"four heptagons",      "4x7",      7, 4, 0,      0, {{4, 3}}},
   {"cube",                "3x4",      4, 3, 0,      2, {{SEE_ALL, SEE_ALL}}},
   {"tetrahedron (buggy)", "3x3",      3, 3, 0,      2, {{SEE_ALL, SEE_ALL}}},
+  {"square grid",         "4x4",      4, 4, 0,      1, {{7, 7}}}
   };
 
diff --git a/classes.h b/classes.h
index ff361ad7..626de7ca 100644
--- a/classes.h
+++ b/classes.h
@@ -187,7 +187,7 @@ enum eLand { laNone, laBarrier, laCrossroads, laDesert, laIce, laCaves, laJungle
   laDual, laSnakeNest
   };
 
-enum eGeometry {gNormal, gEuclid, gSphere, gElliptic, gQuotient, gQuotient2, gTorus, gOctagon, g45, g46, g47, gSmallSphere, gTinySphere, gGUARD};
+enum eGeometry {gNormal, gEuclid, gSphere, gElliptic, gQuotient, gQuotient2, gTorus, gOctagon, g45, g46, g47, gSmallSphere, gTinySphere, gEuclidSquare, gGUARD};
 
 struct geometryinfo {
   const char* name;
diff --git a/geometry.cpp b/geometry.cpp
index 79d1ae23..12622122 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -53,14 +53,37 @@ void precalc() {
     // dynamicval<eGeometry> g(geometry, gNormal);
     // precalc(); }
     // for(int i=0; i<S84; i++) spinmatrix[i] = spin(i * M_PI / S42);
-    crossf = .5;
-    tessf = crossf * sqrt(3);
-    hexf = tessf/3;
-    hcrossf = crossf;
-    hexhexdist = crossf;
-    hexvdist = hexf;
-    hepvdist = crossf;
-    rhexf = hexf;
+    if(a4 && nontruncated) {
+      crossf = .5;
+      hexf = .5;
+      hcrossf = crossf * sqrt(2) / 2;
+      hexhexdist = crossf;
+      hexvdist = hexf;
+      hepvdist = hexf;
+      rhexf = crossf * sqrt(2) / 2;
+      }
+    else if(a4) {
+      ld s2 = sqrt(2);
+      ld xx = 1 - s2 / 2;
+      crossf = .5;
+      tessf = crossf * s2;
+      hexf = .5 * xx * s2;
+      hcrossf = crossf;
+      hexhexdist = crossf * s2;
+      hexvdist = crossf * hypot(1-xx, xx);
+      hepvdist = crossf;
+      rhexf = hexf;
+      }
+    else {
+      crossf = .5;
+      tessf = crossf * sqrt(3);
+      hexf = tessf/3;
+      hcrossf = crossf;
+      hexhexdist = crossf;
+      hexvdist = hexf;
+      hepvdist = crossf;
+      rhexf = hexf;
+      }
     goto finish;
     }
 
diff --git a/graph.cpp b/graph.cpp
index b09cd2c9..fde399c9 100644
--- a/graph.cpp
+++ b/graph.cpp
@@ -158,6 +158,7 @@ void drawSpeed(const transmatrix& V) {
 
 int ctof(cell *c) {
   if(nontruncated) return 1;
+  if(euclid && a4) return !(eupattern(c) & 1);
   // if(euclid) return 0;
   return ishept(c) ? 1 : 0;
   // c->type == 6 ? 0 : 1;
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 02f2f70b..cbbdc886 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -374,26 +374,47 @@ int mindx=-7, mindy=-7, maxdx=7, maxdy=7;
 transmatrix eumove(ld x, ld y) {
   transmatrix Mat = Id;
   Mat[2][2] = 1;
-  Mat[0][2] += (x + y * .5) * eurad;
-  // Mat[2][0] += (x + y * .5) * eurad;
-  Mat[1][2] += y * q3 /2 * eurad;
-  // Mat[2][1] += y * q3 /2 * eurad;
+  
+  if(a4) {
+    Mat[0][2] += x * eurad;
+    Mat[1][2] += y * eurad;
+    }
+  else {
+    Mat[0][2] += (x + y * .5) * eurad;
+    // Mat[2][0] += (x + y * .5) * eurad;
+    Mat[1][2] += y * q3 /2 * eurad;
+    // Mat[2][1] += y * q3 /2 * eurad;
+    }
+  
+  ld v = a4 ? 1 : q3;
+
   while(Mat[0][2] <= -16384 * eurad) Mat[0][2] += 32768 * eurad;
   while(Mat[0][2] >= 16384 * eurad) Mat[0][2] -= 32768 * eurad;
-  while(Mat[1][2] <= -16384 * q3 * eurad) Mat[1][2] += 32768 * q3 * eurad;
-  while(Mat[1][2] >= 16384 * q3 * eurad) Mat[1][2] -= 32768 * q3 * eurad;
+  while(Mat[1][2] <= -16384 * v * eurad) Mat[1][2] += 32768 * v * eurad;
+  while(Mat[1][2] >= 16384 * v * eurad) Mat[1][2] -= 32768 * v * eurad;
   return Mat;
   }
 
 transmatrix eumovedir(int d) {
-  d = fix6(d);
-  switch(d) {
-    case 0: return eumove(1,0);
-    case 1: return eumove(0,1);
-    case 2: return eumove(-1,1);
-    case 3: return eumove(-1,0);
-    case 4: return eumove(0,-1);
-    case 5: return eumove(1,-1);
+  if(a4) {
+    d = d & 3;
+    switch(d) {
+      case 0: return eumove(1,0);
+      case 1: return eumove(0,1);
+      case 2: return eumove(-1,0);
+      case 3: return eumove(0,-1);
+      }
+    }
+  else {
+    d = fix6(d);
+    switch(d) {
+      case 0: return eumove(1,0);
+      case 1: return eumove(0,1);
+      case 2: return eumove(-1,1);
+      case 3: return eumove(-1,0);
+      case 4: return eumove(0,-1);
+      case 5: return eumove(1,-1);
+      }
     }
   return eumove(0,0);
   }
@@ -404,6 +425,7 @@ ld matrixnorm(const transmatrix& Mat) {
   
 void drawEuclidean() {
   DEBB(DF_GRAPH, (debugfile,"drawEuclidean\n"));
+  sphereflip = Id;
   eucoord px=0, py=0;
   if(!centerover) centerover = cwt.c;
   // printf("centerover = %p player = %p [%d,%d]-[%d,%d]\n", lcenterover, cwt.c,
diff --git a/pattern2.cpp b/pattern2.cpp
index 01f96b00..deba9706 100644
--- a/pattern2.cpp
+++ b/pattern2.cpp
@@ -3,6 +3,12 @@
 // Copyright (C) 2011-2017 Zeno Rogue, see 'hyper.cpp' for details
 
 int eupattern(cell *c) {
+  if(a4) {
+    if(torus) return (decodeId(c->master)*2) % 3;
+    eucoord x, y;
+    decodeMaster(c->master, x, y);
+    return (x&1) + (y&1);  
+    }
   if(torus) return (decodeId(c->master)*2) % 3;
   eucoord x, y;
   decodeMaster(c->master, x, y);
@@ -844,7 +850,8 @@ int pattern_threecolor(cell *c) {
     int i = si.id;
     return i >> 2;
     }
-  if(S7 == 4) {
+  if(euclid) return (eupattern(c)+1) % 3;
+  if(S7 == 4 && S3 == 3) {
     int codesN[6] = {0,1,2,1,2,0};
     if(nontruncated) 
       return codesN[c->master->fiftyval];
@@ -872,7 +879,6 @@ int pattern_threecolor(cell *c) {
     }
   if(S7 == 3 && nontruncated)
     return c->master->fiftyval;
-  if(euclid) return (eupattern(c)+1) % 3;
   return !ishept(c);
   }