diff --git a/vis/include/geometry.hpp b/vis/include/geometry.hpp
index 632027d..4f83d82 100644
--- a/vis/include/geometry.hpp
+++ b/vis/include/geometry.hpp
@@ -28,15 +28,10 @@ struct Primitive {
 
     ~Primitive() = default;
 
-    inline void flip() {
-        if (N > 1) std::swap(inds[0], inds[1]);
-    }
-
     void apply(const tc::Cosets<> &table, int gen) {
         for (auto &ind: inds) {
             ind = table.get(ind, gen);
         }
-        flip();
     }
 };
 
@@ -51,15 +46,15 @@ std::vector<size_t> generators(const tc::Group<> &context) {
 
 /**
  * Determine which of g_gens are the correct names for sg_gens within the current context
+ *
+ * Produces the indexes of sg_gens within g_gens; sorted.
  */
 std::vector<size_t> recontext_gens(
     const tc::Group<> &context,
-    std::vector<size_t> g_gens,
-    std::vector<size_t> sg_gens) {
+    const std::vector<size_t> &g_gens,
+    const std::vector<size_t> &sg_gens) {
 
-    std::sort(g_gens.begin(), g_gens.end());
-
-    int inv_gen_map[context.rank()];
+    size_t inv_gen_map[context.rank()];
     for (size_t i = 0; i < g_gens.size(); i++) {
         inv_gen_map[g_gens[i]] = i;
     }
@@ -69,45 +64,10 @@ std::vector<size_t> recontext_gens(
     for (const auto gen : sg_gens) {
         s_sg_gens.push_back(inv_gen_map[gen]);
     }
-    std::sort(s_sg_gens.begin(), s_sg_gens.end());
 
     return s_sg_gens;
 }
 
-/**
- * Determine whether the orientation of the group sg_gens is reversed from the group g_gens within group context
- */
-int get_parity(
-    const tc::Group<> &context,
-    const std::vector<size_t> &g_gens,
-    const std::vector<size_t> &sg_gens
-) {
-    if (g_gens.size() != sg_gens.size() + 1) return 0;
-
-    const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
-
-    int i = 0;
-    for (; i < sg_gens.size(); ++i) {
-        if (proper_sg_gens[i] != i) {
-            break;
-        }
-    }
-
-    return i & 1;
-}
-
-/**
- * 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<size_t> &g_gens,
-    const std::vector<size_t> &sg_gens
-) {
-    const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
-    return context.sub(g_gens).solve(proper_sg_gens);
-}
-
 /**
  * Apply some context transformation to all primitives of this mesh.
  */
@@ -119,16 +79,6 @@ std::vector<Primitive<N>> apply(std::vector<Primitive<N>> prims, const tc::Coset
     return prims;
 }
 
-/**
- * Reverse the orientation of all primitives in this mesh.
- */
-template<unsigned N>
-void flip(std::vector<Primitive<N>> prims) {
-    for (auto &prim : prims) {
-        prim.flip();
-    }
-}
-
 /**
  * Convert the indexes of this mesh to those of a different context, using g_gens to build the parent context and sg_gens to build this context.
  */
@@ -141,26 +91,23 @@ std::vector<Primitive<N>> recontext(
     const std::vector<size_t> &sg_gens
 ) {
     const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
-    const auto table = solve(context, g_gens, {});
-    const auto &cosets = solve(context, sg_gens, {});
+    const auto table = context.sub(g_gens).solve({});
+    const auto cosets = context.sub(sg_gens).solve({});
 
     tc::Path<size_t> path(cosets, proper_sg_gens);
 
     std::vector<size_t> map(path.order());
-    path.walk(0, [&table](size_t coset, size_t gen){
+    path.walk(0, [&table](size_t coset, size_t gen) {
         return table.get(coset, gen);
     }, map.begin());
 
     std::vector<Primitive<N>> res(prims);
-    for (Primitive<N> &prim : res) {
-        for (auto &ind : prim.inds) {
+    for (Primitive<N> &prim: res) {
+        for (auto &ind: prim.inds) {
             ind = map[ind];
         }
     }
 
-    if (get_parity(context, g_gens, sg_gens) == 1)
-        flip(res);
-
     return res;
 }
 
@@ -194,10 +141,11 @@ std::vector<std::vector<Primitive<N>>> each_tile(
     std::vector<Primitive<N>> base = recontext(prims, context, g_gens, sg_gens);
     const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
 
-    const auto table = solve(context, g_gens, {});
-    tc::Path path(solve(context, g_gens, sg_gens));
+    const auto table = context.sub(g_gens).solve({});
 
-    auto _gens = generators(context);
+    const tc::Cosets<> &cosets = context.sub(g_gens).solve(proper_sg_gens);
+
+    tc::Path path(cosets);
 
     std::vector<std::vector<Primitive<N>>> res(path.order());
     path.walk(base, [&](auto from, auto to) {
@@ -227,10 +175,12 @@ template<unsigned N>
 [[nodiscard]]
 std::vector<Primitive<N + 1>> fan(std::vector<Primitive<N>> prims, size_t root) {
     std::vector<Primitive<N + 1>> res(prims.size());
-    std::transform(prims.begin(), prims.end(), res.begin(),
-                   [root](const Primitive<N> &prim) {
-                       return Primitive<N + 1>(prim, root);
-                   }
+    std::transform(
+        prims.begin(), prims.end(),
+        res.begin(),
+        [root](const Primitive<N> &prim) {
+            return Primitive<N + 1>(prim, root);
+        }
     );
     return res;
 }
@@ -243,14 +193,15 @@ std::vector<Primitive<N>> triangulate(
     const tc::Group<> &context,
     const std::vector<size_t> &g_gens
 ) {
-    if (g_gens.size() + 1 != N) // todo make static assert
+    if (g_gens.size() + 1 != N) {
         throw std::logic_error("g_gens size must be one less than N");
+    }
 
-    const auto &combos = Combos(g_gens, g_gens.size() - 1);
+    const auto &combos = Combos<size_t>(g_gens, g_gens.size() - 1U);
 
     std::vector<std::vector<Primitive<N>>> meshes;
 
-    for (const auto &sg_gens : combos) {
+    for (const auto &sg_gens: combos) {
         auto base = triangulate<N - 1>(context, sg_gens);
         auto raised = tile(base, context, g_gens, sg_gens);
         raised.erase(raised.begin(), raised.begin() + base.size());
@@ -260,16 +211,15 @@ std::vector<Primitive<N>> triangulate(
     return merge(meshes);
 }
 
-/**
- * Single-index primitives should not be further triangulated.
- */
+// Single-index primitives should not be further triangulated.
 template<>
 std::vector<Primitive<1>> triangulate(
-    const tc::Group<> &context,
+    const tc::Group<> &,
     const std::vector<size_t> &g_gens
 ) {
-    if (not g_gens.empty()) // todo make static assert
+    if (not g_gens.empty()) {
         throw std::logic_error("g_gens must be empty for a trivial Mesh");
+    }
 
     std::vector<Primitive<1>> res;
     res.emplace_back();
@@ -279,7 +229,9 @@ std::vector<Primitive<1>> triangulate(
 template<unsigned N, class T>
 auto hull(const tc::Group<> &group, T all_sg_gens, const std::vector<std::vector<size_t>> &exclude) {
     std::vector<std::vector<Primitive<N>>> parts;
+
     auto g_gens = generators(group);
+
     for (std::vector<size_t> sg_gens: all_sg_gens) {
         bool excluded = false;
         for (const auto &test: exclude) {