diff --git a/tc/bench/benchmark.cpp b/tc/bench/benchmark.cpp
index 194947f..9149138 100644
--- a/tc/bench/benchmark.cpp
+++ b/tc/bench/benchmark.cpp
@@ -8,8 +8,6 @@
 #include <tc/core.hpp>
 #include <tc/groups.hpp>
 
-#define NAMED(x) #x, x
-
 void bench(
     const std::string &group_expr,
     const std::string &symbol,
diff --git a/tc/include/tc/group.hpp b/tc/include/tc/group.hpp
index 692759e..2c560f3 100644
--- a/tc/include/tc/group.hpp
+++ b/tc/include/tc/group.hpp
@@ -10,6 +10,11 @@ namespace tc {
     struct Group;
     struct SubGroup;
 
+    struct Graph {
+        size_t rank{};
+        std::vector<tc::Rel> edges{};
+    };
+
     /** 
      * @brief Manage the presentation of a Coxeter group and enforce constraints
      * on the multiplicities of its relations.
@@ -28,31 +33,38 @@ namespace tc {
      * <a href="https://en.wikipedia.org/wiki/Coxeter_group#Definition">Coxeter Group (Wikipedia)</a>
      */
     struct Group {
-        int ngens;
-        tc::pair_map<int> _mults;
+        int rank;
+        tc::pair_map<int> _orders;
 
         Group(const Group &) = default;
 
-        explicit Group(int ngens, const std::vector<Rel> &rels = {})
-            : ngens(ngens), _mults(ngens, 2) {
+        explicit Group(int rank, const std::vector<Rel> &rels = {})
+            : rank(rank), _orders(rank, 2) {
 
-            for (int i = 0; i < ngens; ++i) {
+            for (int i = 0; i < rank; ++i) {
                 set(Rel{i, i, 1});
             }
-            
+
             for (const auto &rel: rels) {
                 set(rel);
             }
         }
 
+        explicit Group(const Graph &graph)
+            : rank(graph.rank), _orders(graph.rank, 2) {
+            for (const auto &[i, j, order]: graph.edges) {
+                set({i, j, order});
+            }
+        }
+
         void set(const Rel &r) {
             auto &[i, j, m] = r;
             assert(i != j || m == 1);
-            _mults(i, j) = m;
+            _orders(i, j) = m;
         }
 
         [[nodiscard]] int get(int i, int j) const {
-            return _mults(i, j);
+            return _orders(i, j);
         }
 
         [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
diff --git a/tc/include/tc/groups.hpp b/tc/include/tc/groups.hpp
index a1b7806..e8e8137 100644
--- a/tc/include/tc/groups.hpp
+++ b/tc/include/tc/groups.hpp
@@ -13,7 +13,7 @@ namespace tc {
 
     Group coxeter(const std::string &symbol);
 
-    Group vcoxeter(const std::string &symbol, std::vector<unsigned int> &values);
+    Group vcoxeter(const std::string &symbol, const std::vector<unsigned int> &values);
 
     template<typename ...Args>
     Group coxeter(const std::string &symbol, const Args &... args) {
diff --git a/tc/src/core.cpp b/tc/src/core.cpp
index 64410a0..04bf1a3 100644
--- a/tc/src/core.cpp
+++ b/tc/src/core.cpp
@@ -40,27 +40,31 @@ namespace tc {
         }
     };
 
-    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens, const Coset &bound) {
-        auto ngens = group.ngens;
+    Cosets solve(
+        const Group &group,
+        const std::vector<Gen> &sub_gens,
+        const Coset &bound
+    ) {
+        auto rank = group.rank;
 
         // region Initialize Cosets Table
-        Cosets cosets(ngens);
+        Cosets cosets(rank);
         cosets.add_row();
 
-        if (ngens == 0) {
+        if (rank == 0) {
             cosets.complete = true;
             return cosets;
         }
 
         for (Coset g: sub_gens) {
-            if (g < ngens)
+            if (g < rank)
                 cosets.put(0, g, 0);
         }
         // endregion
 
         // region Initialize Relation Tables
         std::vector<std::tuple<Gen, Gen, Mult>> rels;
-        for (const auto &[i, j, m]: group._mults) {
+        for (const auto &[i, j, m]: group._orders) {
             // The algorithm only works for Coxeter groups; multiplicities m_ii=1 are assumed. Relation tables
             // _may_ be added for them, but they are redundant and hurt performance so are skipped.
             if (i == j) continue;
@@ -75,7 +79,7 @@ namespace tc {
         }
 
         Tables rel_tables(rels);
-        std::vector<std::vector<size_t>> tables_for(ngens);
+        std::vector<std::vector<size_t>> tables_for(rank);
         int rel_idx = 0;
         for (const auto &[i, j, m]: rels) {
             tables_for[i].push_back(rel_idx);
@@ -146,8 +150,8 @@ namespace tc {
 
                 cosets.put(fact_idx, target);
 
-                coset = fact_idx / ngens;
-                gen = fact_idx % ngens;
+                coset = fact_idx / rank;
+                gen = fact_idx % rank;
 
                 // If the product stays within the coset todo
                 for (size_t table_idx: tables_for[gen]) {
@@ -170,7 +174,7 @@ namespace tc {
                             if (trow.gnr == m) {
                                 // loop is closed, but idempotent, so the target links to itself via the other generator.
                                 // todo might be able to move this logic up into the (target == coset) block and avoid those computations.
-                                facts.push(target * ngens + other_gen);
+                                facts.push(target * rank + other_gen);
                             }
                         } else {
                             if (trow.gnr == m - 1) {
@@ -180,7 +184,7 @@ namespace tc {
                                 // loop is closed. We know the last element in the loop must link with this one. 
                                 lst = lst_vals[trow.lst_idx];
 //                            delete trow.lst_ptr;
-                                facts.push(lst * ngens + other_gen);
+                                facts.push(lst * rank + other_gen);
                             }
                         }
                     }
diff --git a/tc/src/groups.cpp b/tc/src/groups.cpp
index e9ae9d5..9b98ac5 100644
--- a/tc/src/groups.cpp
+++ b/tc/src/groups.cpp
@@ -12,7 +12,7 @@ namespace tc {
         return res;
     }
 
-    Group vcoxeter(const std::string &symbol, std::vector<unsigned int> &values) {
+    Group vcoxeter(const std::string &symbol, const std::vector<unsigned int> &values) {
         fmt::dynamic_format_arg_store<fmt::format_context> ds;
 
         for (const auto &value: values) {
diff --git a/tc/src/lang.cpp b/tc/src/lang.cpp
index cd66658..6235909 100644
--- a/tc/src/lang.cpp
+++ b/tc/src/lang.cpp
@@ -80,7 +80,7 @@ struct codegen {
     void loop() {
         ops.emplace_back(Op::LOOP);
     }
-    
+
     void free() {
         ops.emplace_back(Op::FREE);
     }
@@ -221,23 +221,18 @@ std::vector<Op> compile(const std::string &source) {
     return cg.ops;
 }
 
-struct Graph {
-    size_t rank{};
-    std::vector<tc::Rel> edges{};
-};
-
-Graph eval(const std::vector<Op> &ops) {
+tc::Graph eval(const std::vector<Op> &ops) {
     std::vector<std::stack<size_t>> stacks(1);
 
-    Graph g;
+    tc::Graph g;
     stacks.back().emplace(g.rank++);
 
     for (const auto &op: ops) {
         switch (op.code) {
-            case Op::FREE: 
+            case Op::FREE:
             case Op::LINK: {
                 tc::Mult order = tc::FREE;
-                
+
                 if (op.code == Op::LINK) {
                     order = op.value;
                 }
@@ -287,20 +282,7 @@ Graph eval(const std::vector<Op> &ops) {
 namespace tc {
     Group coxeter(const std::string &symbol) {
         auto ops = compile(symbol);
-
-//        fmt::print("#ops: {}\n", ops.size());
-//        for (const auto &op: ops) {
-//            fmt::print(" {}\n", op);
-//        }
-        
         auto diagram = eval(ops);
-
-        Group res((int) diagram.rank);
-
-        for (const auto &[i, j, order]: diagram.edges) {
-            res.set({i, j, order});
-        }
-
-        return res;
+        return Group(diagram);
     }
 }
diff --git a/tc/test/test_lang.cpp b/tc/test/test_lang.cpp
index fc083a4..e9cfd1b 100644
--- a/tc/test/test_lang.cpp
+++ b/tc/test/test_lang.cpp
@@ -20,7 +20,7 @@
 TEST(coxeter, simple) {
     auto g = tc::coxeter("5 3 3");
 
-    ASSERT_EQ(g.ngens, 4);
+    ASSERT_EQ(g.rank, 4);
 
     EXPECT_EQ(g.get(0, 1), 5);
     EXPECT_EQ(g.get(1, 2), 3);
@@ -37,7 +37,7 @@ TEST(coxeter, simple) {
 TEST(coxeter, looping) {
     auto g = tc::coxeter("{5 3 4}");
 
-    ASSERT_EQ(g.ngens, 3);
+    ASSERT_EQ(g.rank, 3);
 
     EXPECT_EQ(g.get(0, 1), 5);
     EXPECT_EQ(g.get(1, 2), 3);
diff --git a/tc/test/test_solve.cpp b/tc/test/test_solve.cpp
index 3cc4f5f..a814771 100644
--- a/tc/test/test_solve.cpp
+++ b/tc/test/test_solve.cpp
@@ -46,12 +46,50 @@ testing::AssertionResult AssertSolveOrder(
     return res;
 }
 
-using namespace tc::group;
-
 #define EXPECT_SOLVE_ORDER(group, sub_gens, expected_order) EXPECT_PRED_FORMAT3(AssertSolveOrder, group, sub_gens, expected_order);
 
 using v = std::vector<tc::Gen>;
 
+tc::Group A(unsigned int n) {
+    return tc::vcoxeter("3 * {}", {n - 1});
+}
+
+tc::Group B(unsigned int n) {
+    return tc::vcoxeter("4 3 * {}", {n - 2});
+}
+
+tc::Group D(unsigned int n) {
+    return tc::vcoxeter("3 * [1 1 {}]", {n - 3});
+}
+
+tc::Group E(unsigned int n) {
+    return tc::vcoxeter("3 * [1 2 {}]", {n - 4});
+}
+
+tc::Group F4() {
+    return tc::coxeter("3 4 3");
+}
+
+tc::Group G2() {
+    return tc::coxeter("6");
+}
+
+tc::Group H(unsigned int n) {
+    return tc::vcoxeter("5 3 * {}", {n - 2});
+}
+
+tc::Group I2(unsigned int n) {
+    return tc::vcoxeter("{}", {n});
+}
+
+tc::Group T(unsigned int m, unsigned int n) {
+    return tc::vcoxeter("{} 2 {}", {m, n});
+}
+
+tc::Group T(unsigned int n) {
+    return T(n, n);
+}
+
 // See the group orders here https://en.wikipedia.org/wiki/Coxeter_group#Properties
 
 TEST(solve, A) {
@@ -95,27 +133,27 @@ TEST(solve, D) {
     EXPECT_SOLVE_ORDER(D(4), v({0, 1, 3}), 8);
     EXPECT_SOLVE_ORDER(D(5), v({}), 1920);
     EXPECT_SOLVE_ORDER(D(5), v({0, 1}), 320);
-    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3}), 160);
-    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3, 4}), 40);
+    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3}), 80);
+    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3, 4}), 16);
     EXPECT_SOLVE_ORDER(D(6), v({}), 23040);
     EXPECT_SOLVE_ORDER(D(6), v({0, 1}), 3840);
-    EXPECT_SOLVE_ORDER(D(6), v({0, 1, 3}), 1920);
+    EXPECT_SOLVE_ORDER(D(6), v({0, 1, 3}), 960);
     EXPECT_SOLVE_ORDER(D(6), v({0, 1, 3, 5}), 480);
 }
 
 TEST(solve, E) {
     EXPECT_SOLVE_ORDER(E(4), v({}), 120);
     EXPECT_SOLVE_ORDER(E(4), v({2}), 60);
-    EXPECT_SOLVE_ORDER(E(4), v({2, 1}), 20);
-    EXPECT_SOLVE_ORDER(E(4), v({2, 1, 3}), 5);
+    EXPECT_SOLVE_ORDER(E(4), v({2, 1}), 30);
+    EXPECT_SOLVE_ORDER(E(4), v({2, 1, 3}), 10);
     EXPECT_SOLVE_ORDER(E(5), v({}), 1920);
     EXPECT_SOLVE_ORDER(E(5), v({2}), 960);
-    EXPECT_SOLVE_ORDER(E(5), v({2, 1}), 320);
-    EXPECT_SOLVE_ORDER(E(5), v({2, 1, 3}), 80);
+    EXPECT_SOLVE_ORDER(E(5), v({2, 1}), 480);
+    EXPECT_SOLVE_ORDER(E(5), v({2, 1, 3}), 160);
     EXPECT_SOLVE_ORDER(E(6), v({}), 51840);
     EXPECT_SOLVE_ORDER(E(6), v({2}), 25920);
-    EXPECT_SOLVE_ORDER(E(6), v({2, 1}), 8640);
-    EXPECT_SOLVE_ORDER(E(6), v({2, 1, 3}), 2160);
+    EXPECT_SOLVE_ORDER(E(6), v({2, 1}), 12960);
+    EXPECT_SOLVE_ORDER(E(6), v({2, 1, 3}), 4320);
 }
 
 TEST(solve, F) {