diff --git a/coxeter.c b/coxeter.c
index 7d8b9a7..10a9e96 100644
--- a/coxeter.c
+++ b/coxeter.c
@@ -144,6 +144,38 @@ int coxeter_order(semisimple_type_t type)
   return order;
 }
 
+int coxeter_hyperplanes(semisimple_type_t type)
+{
+  int hyperplanes = 0;
+  for(int i = 0; i < type.n; i++) {
+    if(type.factors[i].series == 'A') // rank*(rank+1)/2
+      hyperplanes += (type.factors[i].rank * (type.factors[i].rank + 1)) / 2;
+    else if(type.factors[i].series == 'B' || type.factors[i].series == 'C') // rank * rank
+      hyperplanes += type.factors[i].rank * type.factors[i].rank;
+    else if(type.factors[i].series == 'D') // rank * (rank - 1)
+      hyperplanes += type.factors[i].rank * (type.factors[i].rank - 1);
+    else if(type.factors[i].series == 'E') {
+      if(type.factors[i].rank == 6)
+	hyperplanes += 36;
+      else if(type.factors[i].rank == 7)
+	hyperplanes += 63;
+      else if(type.factors[i].rank == 8)
+	hyperplanes += 120;
+      else
+	ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
+    } else if(type.factors[i].series == 'F') {
+      ERROR(type.factors[i].rank != 4, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
+      hyperplanes += 24;
+    } else if(type.factors[i].series == 'G') {
+      ERROR(type.factors[i].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
+      hyperplanes += 6;
+    } else {
+      ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
+    }
+  }
+  return hyperplanes;
+}
+
 static void generate_starting_vector(int rank, gsl_matrix *schlaefli, gsl_vector *result)
 {
   gsl_matrix *schlaefliLU = gsl_matrix_alloc(rank, rank);
@@ -179,7 +211,6 @@ void generate_coxeter_graph(semisimple_type_t type, int *result)
   queue_t queue;
   int current;
 
-
   for(int i = 0; i < rank; i++)
     generators[i] = gsl_matrix_view_array(generators_data + i*rank*rank, rank, rank).matrix;
   for(int i = 0; i < order; i++)
diff --git a/coxeter.h b/coxeter.h
index 36d08c7..babe2e9 100644
--- a/coxeter.h
+++ b/coxeter.h
@@ -13,6 +13,7 @@ typedef struct {
 
 void generate_coxeter_graph(semisimple_type_t type, int *result);
 int coxeter_order(semisimple_type_t type);
+int coxeter_hyperplanes(semisimple_type_t type);
 int coxeter_rank(semisimple_type_t type);
 
 #endif
diff --git a/generate.c b/generate.c
index 7679630..cf90399 100644
--- a/generate.c
+++ b/generate.c
@@ -52,10 +52,7 @@ int main(int argc, const char *argv[])
 
   // print stuff
 
-  int hyperplane_count = 0;
-  for(int i = 0; i < order; i++)
-    if(graph[i].is_hyperplane_reflection)
-      hyperplane_count++;
+  int hyperplane_count = coxeter_hyperplanes(type);
 
   fprintf(stderr, "Rank: %d\t\tOrder: %d\t\tHyperplanes: %d\n", rank, order, hyperplane_count);
   fprintf(stderr, "\n");
diff --git a/thickenings.c b/thickenings.c
index c6a0d8b..8398f21 100644
--- a/thickenings.c
+++ b/thickenings.c
@@ -12,6 +12,12 @@
 
 char *alphabetize(int *word, int len, const char *alphabet, char *buffer)
 {
+  if(len == 0) {
+    buffer[0] = '1';
+    buffer[1] = 0;
+    return buffer;
+  }
+
   int i = 0;
   for(i = 0; i < len; i++)
     buffer[i] = alphabet[word[i]];