diff --git a/libs/geom/CMakeLists.txt b/libs/geom/CMakeLists.txt
index e71c70f6..ec2122ff 100644
--- a/libs/geom/CMakeLists.txt
+++ b/libs/geom/CMakeLists.txt
@@ -10,7 +10,7 @@ file(GLOB_RECURSE PSEMEK_GEOM_SOURCES "source/*.cpp")
 
 psemek_add_library(psemek-geom ${PSEMEK_GEOM_HEADERS} ${PSEMEK_GEOM_SOURCES})
 target_include_directories(psemek-geom PUBLIC "${CMAKE_CURRENT_SOURCE_DIR}/include")
-target_link_libraries(psemek-geom PUBLIC psemek-util Boost::boost)
+target_link_libraries(psemek-geom PUBLIC psemek-util psemek-group Boost::boost)
 if(PSEMEK_ROBUST_PREDICATES)
 	target_link_libraries(psemek-geom PUBLIC gmp)
 endif()
diff --git a/libs/geom/include/psemek/geom/symmetry.hpp b/libs/geom/include/psemek/geom/symmetry.hpp
new file mode 100644
index 00000000..619be3f5
--- /dev/null
+++ b/libs/geom/include/psemek/geom/symmetry.hpp
@@ -0,0 +1,155 @@
+#pragma once
+
+#include <psemek/group/cyclic.hpp>
+#include <psemek/group/dihedral.hpp>
+
+#include <psemek/geom/affine_transform.hpp>
+#include <psemek/geom/quaternion.hpp>
+
+#include <psemek/util/assert.hpp>
+
+namespace psemek::geom
+{
+
+	template <typename T, std::size_t N>
+	struct symmetry
+	{
+		matrix<T, N, N> m;
+
+		symmetry();
+		symmetry(symmetry const &) = default;
+
+		template <std::size_t D, typename Repr>
+		symmetry(group::cyclic<D, Repr> const & g);
+
+		template <std::size_t D, typename Repr>
+		symmetry(group::cyclic<D, Repr> const & g, std::size_t i, std::size_t j);
+
+		template <std::size_t D, typename Repr>
+		symmetry(group::dihedral<D, Repr> const & g);
+
+		template <std::size_t D, typename Repr>
+		symmetry(group::dihedral<D, Repr> const & g, std::size_t i, std::size_t j);
+
+		matrix<T, N, N + 1> affine_matrix() const;
+		matrix<T, N, N> linear_matrix() const;
+		vector<T, N> translation_vector() const;
+		matrix<T, N + 1, N + 1> homogeneous_matrix() const;
+
+		affine_transform<T, N, N> transform() const;
+
+		vector<T, N> operator()(vector<T, N> const & v) const;
+		point<T, N> operator()(point<T, N> const & p) const;
+	};
+
+	template <typename T, std::size_t N>
+	symmetry<T, N>::symmetry()
+	{
+		m = m.identity();
+	}
+
+	template <typename T, std::size_t N>
+	template <std::size_t D, typename Repr>
+	symmetry<T, N>::symmetry(group::cyclic<D, Repr> const & g)
+		: symmetry(g, 0, 1)
+	{}
+
+	template <typename T, std::size_t N>
+	template <std::size_t D, typename Repr>
+	symmetry<T, N>::symmetry(group::cyclic<D, Repr> const & g, std::size_t i, std::size_t j)
+	{
+		m = m.identity();
+
+		T angle = (T{2} * geom::pi * static_cast<T>(g.value())) / static_cast<T>(D);
+
+		m[i][i] =  std::cos(angle);
+		m[i][j] = -std::sin(angle);
+		m[j][i] =  std::sin(angle);
+		m[j][j] =  std::cos(angle);
+	}
+
+	template <typename T, std::size_t N>
+	template <std::size_t D, typename Repr>
+	symmetry<T, N>::symmetry(group::dihedral<D, Repr> const & g)
+		: symmetry(g, 0, 1)
+	{}
+
+	template <typename T, std::size_t N>
+	template <std::size_t D, typename Repr>
+	symmetry<T, N>::symmetry(group::dihedral<D, Repr> const & g, std::size_t i, std::size_t j)
+	{
+		m = m.identity();
+
+		T angle = (T{2} * geom::pi * static_cast<T>(g.value())) / static_cast<T>(D);
+
+		// See https://en.wikipedia.org/wiki/Dihedral_group#Matrix_representation
+
+		if (g.is_rotation())
+		{
+			m[i][i] =  std::cos(angle);
+			m[i][j] = -std::sin(angle);
+			m[j][i] =  std::sin(angle);
+			m[j][j] =  std::cos(angle);
+		}
+		else
+		{
+			m[i][i] =  std::cos(angle);
+			m[i][j] =  std::sin(angle);
+			m[j][i] =  std::sin(angle);
+			m[j][j] = -std::cos(angle);
+		}
+	}
+
+	template <typename T, std::size_t N>
+	matrix<T, N, N + 1> symmetry<T, N>::affine_matrix() const
+	{
+		matrix<T, N, N + 1> result;
+		for (std::size_t i = 0; i < N; ++i)
+			for (std::size_t j = 0; j < N; ++j)
+				result[i][j] = m[i][j];
+		for (std::size_t i = 0; i < N; ++i)
+			result[i][N] = T{0};
+		return result;
+	}
+
+	template <typename T, std::size_t N>
+	matrix<T, N, N> symmetry<T, N>::linear_matrix() const
+	{
+		return m;
+	}
+
+	template <typename T, std::size_t N>
+	vector<T, N> symmetry<T, N>::translation_vector() const
+	{
+		return vector<T, N>::zero();
+	}
+
+	template <typename T, std::size_t N>
+	matrix<T, N + 1, N + 1> symmetry<T, N>::homogeneous_matrix() const
+	{
+		auto result = matrix<T, N + 1, N + 1>::identity();
+		for (std::size_t i = 0; i < N; ++i)
+			for (std::size_t j = 0; j < N; ++j)
+				result[i][j] = m[i][j];
+		return result;
+	}
+
+	template <typename T, std::size_t N>
+	affine_transform<T, N, N> symmetry<T, N>::transform() const
+	{
+		return {m, geom::vector<T, N>::zero()};
+	}
+
+	template <typename T, std::size_t N>
+	vector<T, N> symmetry<T, N>::operator()(vector<T, N> const & v) const
+	{
+		return m * v;
+	}
+
+	template <typename T, std::size_t N>
+	point<T, N> symmetry<T, N>::operator()(point<T, N> const & p) const
+	{
+		return p.zero() + m * (p - p.zero());
+	}
+
+}