diff --git a/cosets/src/main.cpp b/cosets/src/main.cpp
index 37e45ee..041b78a 100644
--- a/cosets/src/main.cpp
+++ b/cosets/src/main.cpp
@@ -44,9 +44,9 @@ public:
       u_view = glGetUniformLocation(program, "view");
       u_color = glGetUniformLocation(program, "color");
 
-      const int N = 3;
-      const Mults &mults = schlafli<N>({5, 3});
-      vert_data = vertices<N>(mults, {10, 1, 1});
+      const int N = 4;
+      const Mults &mults = schlafli<N>({5, 3, 3});
+      vert_data = vertices<N>(mults, {10, });
       edge_data = edges<N>(mults);
       face_data = faces<N>(mults);
 
diff --git a/cosets/src/util/coxeter.hpp b/cosets/src/util/coxeter.hpp
index f385992..6122f3f 100644
--- a/cosets/src/util/coxeter.hpp
+++ b/cosets/src/util/coxeter.hpp
@@ -62,19 +62,26 @@ Mults schlafli(const int (&symbol)[N - 1]) {
 
 struct Table {
    const std::vector<int> gens;
+   std::vector<int> gen_inds;
    std::vector<std::vector<int>> fwd{};
    std::vector<std::vector<int>> rev{};
 
    explicit Table(const std::vector<int> gens) : gens(gens) {
       add_row();
+
+      gen_inds = std::vector<int>(gens[gens.size() - 1] + 1, -1);
+      for (int i = 0; i < gens.size(); i++) {
+         gen_inds[gens[i]] = i;
+      }
    }
 
    [[nodiscard]] int gen_index(int gen) const {
-      for (unsigned i = 0; i < gens.size(); ++i)
-         if (gens[i] == gen)
-            return i;
-
-      throw std::logic_error("Referencing nonexistant generator");
+      if (gen >= gen_inds.size())
+         throw std::logic_error("Referencing nonexistant generator (too large)");
+      int i = gen_inds[gen];
+      if (i < 0)
+         throw std::logic_error("Referencing nonexistant generator (not present)");
+      return i;
    }
 
    void add_row() {