diff --git a/cosets/CMakeLists.txt b/cosets/CMakeLists.txt
index 4e40d31..e157ee6 100644
--- a/cosets/CMakeLists.txt
+++ b/cosets/CMakeLists.txt
@@ -16,3 +16,5 @@ add_custom_command(
 add_executable(coxeter src/coxeter.cpp)
 add_executable(mirror src/mirrors.cpp)
 target_link_libraries(mirror PRIVATE glm)
+add_executable(mesh src/mesh.cpp)
+target_link_libraries(mesh PRIVATE glm)
diff --git a/cosets/src/main.cpp b/cosets/src/main.cpp
index de0e007..c7e7c88 100644
--- a/cosets/src/main.cpp
+++ b/cosets/src/main.cpp
@@ -5,6 +5,9 @@
 #include <glm/gtc/type_ptr.hpp>
 #include <glm/gtx/string_cast.hpp>
 #include <glm/gtc/matrix_transform.hpp>
+#include <vector>
+
+#include "util/mesh.hpp"
 
 using namespace std;
 
@@ -13,7 +16,7 @@ class CosetsWindow : public Window {
    GLuint tri;
 
    GLuint verts;
-   static const unsigned VERTS_N = 8;
+   std::vector<glm::vec4> verts_data;
 
 public:
    void init() override {
@@ -29,21 +32,16 @@ public:
 
       program = build_program("main", vs, fs);
 
-      glm::vec4 verts_data[VERTS_N]{
-         {+0.5, +0.5, +0.5, +0.0},
-         {+0.5, -0.5, +0.5, +0.0},
-         {-0.5, -0.5, +0.5, +0.0},
-         {-0.5, +0.5, +0.5, +0.0},
-
-         {+0.5, +0.5, +0.5, -0.5},
-         {+0.5, -0.5, +0.5, -0.5},
-         {-0.5, -0.5, +0.5, +0.5},
-         {-0.5, +0.5, +0.5, +0.5},
-      };
+      verts_data = vertices<3>({}, Multiplicites<3>({
+         {0, 1, 4},
+         {1, 2, 3}
+      }), {
+         2.0f, .05f, 0.05f
+      });
 
       glGenBuffers(1, &verts);
       glBindBuffer(GL_ARRAY_BUFFER, verts);
-      glBufferData(GL_ARRAY_BUFFER, sizeof(float) * 4 * VERTS_N, verts_data, GL_STATIC_DRAW);
+      glBufferData(GL_ARRAY_BUFFER, sizeof(glm::vec4) * verts_data.size(), &verts_data[0], GL_STATIC_DRAW);
 
 
       glGenVertexArrays(1, &tri);
@@ -78,7 +76,7 @@ public:
       glPointSize(10.f);
 
       glBindVertexArray(tri);
-      glDrawArrays(GL_POINTS, 0, VERTS_N);
+      glDrawArrays(GL_POINTS, 0, verts_data.size());
 
       swapbuffers();
    }
diff --git a/cosets/src/mesh.cpp b/cosets/src/mesh.cpp
new file mode 100644
index 0000000..eb26070
--- /dev/null
+++ b/cosets/src/mesh.cpp
@@ -0,0 +1,16 @@
+#include "util/mesh.hpp"
+
+int main(int argc, char *argv[]) {
+   auto vs = vertices<3>({}, Multiplicites<3>({
+      {0, 1, 4},
+      {1, 2, 3}
+   }), {
+      1.0f, 1.0f, 1.0f
+   });
+
+   for (const auto &v : vs) {
+      std::cout << glm::to_string(v) << std::endl;
+   }
+
+   return 0;
+}
\ No newline at end of file
diff --git a/cosets/src/util/mesh.hpp b/cosets/src/util/mesh.hpp
new file mode 100644
index 0000000..5879526
--- /dev/null
+++ b/cosets/src/util/mesh.hpp
@@ -0,0 +1,60 @@
+#pragma once
+
+#include "coxeter.hpp"
+#include "mirrors.hpp"
+#include "numeric.hpp"
+
+#include <vector>
+
+template<int N>
+std::vector<glm::vec4>
+vertices(const std::vector<int> &subgens, const Multiplicites<N> &mults, const float (&coords)[N]) {
+   std::vector<std::vector<int>> rels{};
+   rels.reserve(N + N * (N - 1) / 2);
+
+   for (int i = 0; i < N; ++i) {
+      rels.push_back({i, i});
+   }
+   for (int a = 0; a < N; ++a) {
+      for (int b = 0; b < a; ++b) {
+         int mult = mults.get(a, b);
+
+         std::vector<int> rel{};
+         for (int i = 0; i < mult; ++i) {
+            rel.push_back(a);
+            rel.push_back(b);
+         }
+         rels.push_back(rel);
+      }
+   }
+
+   Table *table = solve(N, subgens, rels);
+
+//   std::cout << table->size() << std::endl;
+//   std::cout << *table << std::endl;
+
+//   for (const auto &v : table->words()) {
+//      std::cout << "[ ";
+//      for (auto e : v) {
+//         std::cout << e << " ";
+//      }
+//      std::cout << "]\n";
+//   }
+
+   const std::vector<glm::vec4> &normals = mirror<3>(mults);
+   const std::vector<glm::vec4> &corners = plane_intersections(normals);
+   const std::vector<float> coords_vec(coords, coords + N);
+   const glm::vec4 &identity = glm::normalize(barycentric(corners, coords_vec));
+
+   std::vector<glm::vec4> verts(table->size());
+
+   for (const auto &word : table->words()) {
+      glm::vec4 vert = identity;
+      for (const auto &gen : word) {
+         vert = reflect(vert, normals[gen]);
+      }
+      verts.push_back(vert);
+   }
+
+   return verts;
+}
\ No newline at end of file
diff --git a/cosets/src/util/numeric.hpp b/cosets/src/util/numeric.hpp
index d4a749f..b787c08 100644
--- a/cosets/src/util/numeric.hpp
+++ b/cosets/src/util/numeric.hpp
@@ -51,7 +51,7 @@ std::vector<glm::vec4> plane_intersections(std::vector<glm::vec4> normals) {
    std::vector<glm::vec4> results(N);
 
    for (int i = 0; i < N; ++i) {
-      results[i] = gram_schmidt_last(normals);
+      results[i] = glm::normalize(gram_schmidt_last(normals));
       std::rotate(normals.begin(), normals.begin() + 1, normals.end());
    }