optimize vertex generation; break edge/face generation

cosets/include/mirrors.hpp

@@ -2,6 +2,31 @@
 
 #include <vector>
 #include <glm/glm.hpp>
-#include "coxeter.hpp"
+#include <cmath>
 
-std::vector<glm::vec4> mirror(const Mults &mults);
+#include "coxeter.hpp"
+#include "numeric.hpp"
+
+template<int NGENS>
+std::vector<glm::vec4> mirror(const Mults<NGENS> &mults) {
+    std::vector<glm::vec4> mirrors{};
+    for (int p = 0; p < NGENS; ++p) {
+        glm::vec4 vp{};
+        for (int m = 0; m < p; ++m) {
+            glm::vec4 vq = mirrors[m];
+            vp[m] = (cos(M_PI / mults.get(p, m)) - dot(m, vp, vq)) / vq[m];
+        }
+        vp[p] = std::sqrt(1 - glm::dot(vp, vp));
+
+        for (const auto &v : mirrors) {
+            if (glm::dot(vp, v) > 0) {
+                vp *= -1;
+                break;
+            }
+        }
+
+        mirrors.push_back(round(vp, 15));
+    }
+
+    return mirrors;
+}