diff --git a/tc/include/tc/core.hpp b/tc/include/tc/core.hpp
index 89ab80b..8d2268e 100644
--- a/tc/include/tc/core.hpp
+++ b/tc/include/tc/core.hpp
@@ -11,4 +11,20 @@
 
 namespace tc {
     Cosets solve(const Group &group, const std::vector<Gen> &sub_gens, const Coset &bound = UNBOUNDED);
+    
+    // todo
+    ///**
+    // * Solve the cosets generated by sg_gens within the subgroup generated by g_gens of the group context
+    // */
+    //    tc::Cosets solve(
+    //        const tc::Group &context,
+    //        const std::vector<tc::Gen> &g_gens,
+    //        const std::vector<tc::Gen> &sg_gens
+    //    ) {
+    //        // todo this should also be handled with 'global' generators.
+    //        const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
+    //
+    //        return tc::solve(context.subgroup(g_gens), proper_sg_gens);
+    //    }
+
 }
diff --git a/tc/include/tc/group.hpp b/tc/include/tc/group.hpp
index 2c560f3..81eff7a 100644
--- a/tc/include/tc/group.hpp
+++ b/tc/include/tc/group.hpp
@@ -67,14 +67,14 @@ namespace tc {
             return _orders(i, j);
         }
 
-        [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
+        [[nodiscard]] SubGroup subgroup(const std::vector<tc::Gen> &gens) const;
     };
 
     struct SubGroup : public Group {
-        std::vector<int> gen_map;
+        std::vector<tc::Gen> gen_map;
         const Group &parent;
 
-        SubGroup(const Group &parent, std::vector<int> gen_map)
+        SubGroup(const Group &parent, std::vector<tc::Gen> gen_map)
             : Group(gen_map.size()), parent(parent), gen_map() {
 
             std::sort(gen_map.begin(), gen_map.end());
diff --git a/tc/src/core.cpp b/tc/src/core.cpp
index 04bf1a3..0808e59 100644
--- a/tc/src/core.cpp
+++ b/tc/src/core.cpp
@@ -6,7 +6,7 @@
 #include <vector>
 
 namespace tc {
-    SubGroup Group::subgroup(const std::vector<int> &gens) const {
+    SubGroup Group::subgroup(const std::vector<tc::Gen> &gens) const {
         return {*this, gens};
     }
 
diff --git a/vis/include/geo/solver.hpp b/vis/include/geo/solver.hpp
index 7c6c897..7939b3b 100644
--- a/vis/include/geo/solver.hpp
+++ b/vis/include/geo/solver.hpp
@@ -11,12 +11,12 @@
 #include "combo.hpp"
 
 /**
- * Produce a list of all generators for the group context. The range [0..group.ngens).
+ * Produce a list of all generators for the group context. The range [0..group.rank).
  */
-std::vector<int> generators(const tc::Group &context) {
+std::vector<tc::Gen> generators(const tc::Group &context) {
     // todo if tc::Group has 'global' generators, then this will be a member of tc::Group.
     //  std::iota would populate a 'default' list of names, if names are not provided.
-    std::vector<int> g_gens(context.ngens);
+    std::vector<tc::Gen> g_gens(context.rank);
     std::iota(g_gens.begin(), g_gens.end(), 0);
     return g_gens;
 }
@@ -24,20 +24,20 @@ std::vector<int> generators(const tc::Group &context) {
 /**
  * Determine which of g_gens are the correct names for sg_gens within the current context
  */
-std::vector<int> recontext_gens(
+std::vector<tc::Gen> recontext_gens(
     const tc::Group &context,
-    std::vector<int> g_gens,
-    std::vector<int> sg_gens) {
+    std::vector<tc::Gen> g_gens,
+    std::vector<tc::Gen> sg_gens) {
     // todo ideally tc::Group will deal in 'global' generators so this stell will be unecessary.
 
     std::sort(g_gens.begin(), g_gens.end());
 
-    int inv_gen_map[context.ngens];
+    tc::Gen inv_gen_map[context.rank];
     for (size_t i = 0; i < g_gens.size(); i++) {
         inv_gen_map[g_gens[i]] = i;
     }
 
-    std::vector<int> s_sg_gens;
+    std::vector<tc::Gen> s_sg_gens;
     s_sg_gens.reserve(sg_gens.size());
     for (const auto gen: sg_gens) {
         s_sg_gens.push_back(inv_gen_map[gen]);
@@ -52,21 +52,22 @@ std::vector<int> recontext_gens(
  */
 tc::Cosets solve(
     const tc::Group &context,
-    const std::vector<int> &g_gens,
-    const std::vector<int> &sg_gens
+    const std::vector<tc::Gen> &g_gens,
+    const std::vector<tc::Gen> &sg_gens
 ) {
     // todo this should also be handled with 'global' generators.
     const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
-    return context.subgroup(g_gens).solve(proper_sg_gens);
+    
+    return tc::solve(context.subgroup(g_gens), proper_sg_gens);
 }
 
 /**
  * Apply some context transformation to all primitives of this mesh.
  */
 template<unsigned N>
-void apply(const tc::Cosets &table, int gen, Prims<N> &mat) {
+void apply(const tc::Cosets &table, tc::Gen gen, Prims<N> &mat) {
     auto data = mat.data();
-    for (int i = 0; i < mat.size(); ++i) {
+    for (tc::Gen i = 0; i < mat.size(); ++i) {
         data[i] = table.get(data[i], gen);
     }
 }
@@ -79,15 +80,15 @@ template<unsigned N>
 Prims<N> recontext(
     Prims<N> prims,
     const tc::Group &context,
-    const std::vector<int> &g_gens,
-    const std::vector<int> &sg_gens
+    const std::vector<tc::Gen> &g_gens,
+    const std::vector<tc::Gen> &sg_gens
 ) {
     // todo this will be simpler with 'global' gens, but it's still not free...
     const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
     const auto table = solve(context, g_gens, {});
     const auto path = solve(context, sg_gens, {}).path;
 
-    auto map = path.template walk<int, int>(0, proper_sg_gens, [table](int coset, int gen) {
+    auto map = path.template walk<tc::Coset, tc::Gen>(0, proper_sg_gens, [table](tc::Coset coset, tc::Gen gen) {
         return table.get(coset, gen);
     });
 
@@ -127,8 +128,8 @@ template<unsigned N>
 std::vector<Prims<N>> tile(
     Prims<N> prims,
     const tc::Group &context,
-    const std::vector<int> &g_gens,
-    const std::vector<int> &sg_gens
+    const std::vector<tc::Gen> &g_gens,
+    const std::vector<tc::Gen> &sg_gens
 ) {
     // todo convert to nullaryexpr.
     //  some stuff will be easier with global generators, but not all.
@@ -138,11 +139,11 @@ std::vector<Prims<N>> tile(
     const auto table = solve(context, g_gens, {});
     const auto path = solve(context, g_gens, sg_gens).path;
 
-    std::vector<int> _gens = generators(context);
+    std::vector<tc::Gen> _gens = generators(context);
 
-    std::vector<Prims<N>> res = path.walk<Prims<N>, int>(
+    std::vector<Prims<N>> res = path.walk<Prims<N>, tc::Gen>(
         base, _gens,
-        [&](Prims<N> from, int gen) {
+        [&](Prims<N> from, tc::Gen gen) {
             apply<N>(table, gen, from);
             return from;
         }
@@ -172,7 +173,7 @@ Prims<N + 1> fan(Prims<N> prims, int root) {
 template<unsigned N>
 Prims<N> triangulate(
     const tc::Group &context,
-    const std::vector<int> &g_gens
+    const std::vector<tc::Gen> &g_gens
 ) {
     // todo (?) might be possible with nullaryexpr
     //  not so sure, though.
@@ -201,7 +202,7 @@ Prims<N> triangulate(
 template<>
 Prims<1> triangulate<1>(
     const tc::Group &context,
-    const std::vector<int> &g_gens
+    const std::vector<tc::Gen> &g_gens
 ) {
     if (not g_gens.empty()) // todo make static assert
         throw std::logic_error("g_gens must be empty for a trivial Mesh");
@@ -210,10 +211,10 @@ Prims<1> triangulate<1>(
 }
 
 template<unsigned N, class T>
-auto hull(const tc::Group &group, T all_sg_gens, const std::vector<std::vector<int>> &exclude) {
+auto hull(const tc::Group &group, T all_sg_gens, const std::vector<std::vector<tc::Gen>> &exclude) {
     std::vector<Prims<N>> parts;
     auto g_gens = generators(group);
-    for (const std::vector<int> &sg_gens: all_sg_gens) {
+    for (const std::vector<tc::Gen> &sg_gens: all_sg_gens) {
         bool excluded = false;
         for (const auto &test: exclude) {
             if (sg_gens == test) {
diff --git a/vis/include/gl/vertexarray.hpp b/vis/include/gl/vertexarray.hpp
index 7b863e6..e9b395c 100644
--- a/vis/include/gl/vertexarray.hpp
+++ b/vis/include/gl/vertexarray.hpp
@@ -15,6 +15,7 @@ public:
 
 private:
     GLuint id = 0;
+    GLuint count = 0;
 
     template<size_t ...idx>
     inline void formatall(
diff --git a/vis/src/main.cpp b/vis/src/main.cpp
index f329443..aa66478 100644
--- a/vis/src/main.cpp
+++ b/vis/src/main.cpp
@@ -118,23 +118,34 @@ void set_style() {
 int run(GLFWwindow *window, ImGuiContext *context) {
     State state;
 
+    PointCloud pc;
+    LineCloud lc;
     PointRenderer<Eigen::Vector4f> point_render;
+    LineRenderer<Eigen::Vector4f> line_render;
 
     {
         tc::Group group = tc::coxeter("3 4 3");
         Eigen::Vector4f coords{1, 1, 1, 1};
 
         auto cosets = tc::solve(group, {}, 1000000);
-        
+
         auto mirrors = mirror<4>(group);
 
         auto corners = plane_intersections(mirrors);
         auto start = barycentric(corners, coords);
         start.normalize();
-        
+
         auto points = cosets.path.walk<vec4, vec4>(start, mirrors, reflect<vec4>);
 
-        point_render.upload(points);
+        std::vector<unsigned> edges = {
+            0, 1,
+            0, 2,
+            0, 3,
+            0, 4,
+        };
+
+        pc.upload(points);
+        lc.upload(points, edges);
     }
 
     glEnable(GL_DEPTH_TEST);
@@ -158,7 +169,8 @@ int run(GLFWwindow *window, ImGuiContext *context) {
         auto aspect = (float) display_h / (float) display_w;
         state.proj = Eigen::AlignedScaling3f(aspect, 1.0, -0.6);
 
-        point_render.draw(state);
+        point_render.draw(pc, state);
+        line_render.draw(lc, state);
 
         ImGui_ImplOpenGL3_RenderDrawData(ImGui::GetDrawData());
         glfwSwapBuffers(window);
diff --git a/vis/src/render/pointrender.hpp b/vis/src/render/pointrender.hpp
index a950172..55a9c16 100644
--- a/vis/src/render/pointrender.hpp
+++ b/vis/src/render/pointrender.hpp
@@ -18,18 +18,13 @@ struct State {
 };
 
 template<typename V_=Eigen::Vector4f>
-struct PointRenderer {
+struct PointCloud {
     using Vertex = V_;
 
-    VertexShader vs{std::ifstream("res/shaders/main.vert.glsl")};
-    FragmentShader fs{std::ifstream("res/shaders/main.frag.glsl")};
-
-    Program pgm{vs, fs};
-
     Buffer<Vertex> vbo;
     VertexArray<Vertex> vao{vbo};
 
-    GLuint count;
+    GLuint count{};
 
     template<typename T>
     void upload(const T &points) {
@@ -38,15 +33,69 @@ struct PointRenderer {
 //    Buffer<GLuint> ind_buf;
 //    glVertexArrayElementBuffer(vao, ind_buf);
     }
+};
 
-    void draw(const State &state) {
+template<typename V_=Eigen::Vector4f>
+struct PointRenderer {
+    using Vertex = V_;
+
+    VertexShader vs{std::ifstream("res/shaders/main.vert.glsl")};
+    FragmentShader fs{std::ifstream("res/shaders/main.frag.glsl")};
+
+    Program pgm{vs, fs};
+
+    void draw(const PointCloud<Vertex> &obj, const State &state) {
         glUseProgram(pgm);
-        glBindVertexArray(vao);
+        glBindVertexArray(obj.vao);
         glUniform4fv(0, 1, state.fg.data());
         glUniform1f(1, state.time);
         glUniformMatrix4fv(2, 1, false, state.proj.data());
         glUniformMatrix4fv(3, 1, false, state.view.data());
-        glDrawArrays(GL_POINTS, 0, count);
+        glDrawArrays(GL_POINTS, 0, obj.count);
+        glBindVertexArray(0);
+        glUseProgram(0);
+    }
+};
+
+template<typename V_=Eigen::Vector4f>
+struct LineCloud {
+    using Vertex = V_;
+    
+    Buffer<Vertex> vbo{};
+    Buffer<unsigned> ibo{};
+    VertexArray<Vertex> vao{vbo};
+
+    GLuint count{};
+
+    LineCloud() {
+        glVertexArrayElementBuffer(vao, ibo);
+    }
+
+    template<typename T, typename U>
+    void upload(const T &points, const U &inds) {
+        vbo.upload(points);
+        
+        count = ibo.upload(inds);
+    }
+};
+
+template<typename V_=Eigen::Vector4f>
+struct LineRenderer {
+    using Vertex = V_;
+
+    VertexShader vs{std::ifstream("res/shaders/main.vert.glsl")};
+    FragmentShader fs{std::ifstream("res/shaders/main.frag.glsl")};
+    
+    Program pgm{vs, fs};
+    
+    void draw(const LineCloud<Vertex> &obj, const State &state) {
+        glUseProgram(pgm);
+        glBindVertexArray(obj.vao);
+        glUniform4fv(0, 1, state.fg.data());
+        glUniform1f(1, state.time);
+        glUniformMatrix4fv(2, 1, false, state.proj.data());
+        glUniformMatrix4fv(3, 1, false, state.view.data());
+        glDrawElements(GL_LINES, obj.count, GL_UNSIGNED_INT, nullptr);
         glBindVertexArray(0);
         glUseProgram(0);
     }