diff --git a/src/core_ffi/python_ffi/binder/fast_cal.cc b/src/core_ffi/python_ffi/binder/fast_cal.cc
index 3afe1dd..24a5dfd 100644
--- a/src/core_ffi/python_ffi/binder/fast_cal.cc
+++ b/src/core_ffi/python_ffi/binder/fast_cal.cc
@@ -1,3 +1,4 @@
+#include <pybind11/stl.h>
 #include <py_ffi/fast_cal.h>
 
 #include "binder.h"
diff --git a/src/core_ffi/python_ffi/binder/group.cc b/src/core_ffi/python_ffi/binder/group.cc
index 3874b1b..24d239a 100644
--- a/src/core_ffi/python_ffi/binder/group.cc
+++ b/src/core_ffi/python_ffi/binder/group.cc
@@ -20,6 +20,7 @@ void bind_group(const py::module_ &m) {
         .def_property_readonly("pattern_id", &PyGroup::pattern_id)
 
         .def("__str__", &PyGroup::to_string)
+        .def("__repr__", &PyGroup::repr)
 
         .def("cases", &PyGroup::cases)
         .def("to_vertical_mirror", &PyGroup::to_vertical_mirror)
diff --git a/src/core_ffi/python_ffi/binder/klsk_cases.cc b/src/core_ffi/python_ffi/binder/klsk_cases.cc
index ebc3f07..14db198 100644
--- a/src/core_ffi/python_ffi/binder/klsk_cases.cc
+++ b/src/core_ffi/python_ffi/binder/klsk_cases.cc
@@ -2,6 +2,7 @@
 
 #include "binder.h"
 #include "py_ffi/cases.h"
+#include "py_ffi/layout.h"
 
 using klotski::ffi::PyCases;
 using klotski::ffi::PyCasesIter;
diff --git a/src/core_ffi/python_ffi/binder/klsk_code.cc b/src/core_ffi/python_ffi/binder/klsk_code.cc
index 4b3e1f5..a278c63 100644
--- a/src/core_ffi/python_ffi/binder/klsk_code.cc
+++ b/src/core_ffi/python_ffi/binder/klsk_code.cc
@@ -8,6 +8,7 @@
 
 using klotski::ffi::PyBlock;
 using klotski::ffi::PyLayout;
+using klotski::ffi::PyToward;
 using klotski::ffi::PySpeedUp;
 using klotski::ffi::PyShortCode;
 
@@ -30,6 +31,12 @@ static void bind_layout(const py::module_ &mod) {
         .value("B_2x2", PyBlock::B_2x2)
         .value("FILL", PyBlock::FILL);
 
+    py::enum_<PyToward>(mod, "Toward")
+        .value("A", PyToward::A)
+        .value("B", PyToward::B)
+        .value("C", PyToward::C)
+        .value("D", PyToward::D);
+
     py::class_<PyLayout>(mod, "Layout")
         .def(py::init<uint64_t>())
         .def(py::init<PyShortCode>())
@@ -55,7 +62,17 @@ static void bind_layout(const py::module_ &mod) {
         .def("to_string", &PyLayout::string, py::arg("shorten") = false)
 
         .def_property_readonly("value", &PyLayout::value)
-        // TODO: add n_1x1 / n_1x2 / n_2x1 / ...
+        .def_property_readonly("n_1x1", &PyLayout::n_1x1)
+        .def_property_readonly("n_1x2", &PyLayout::n_1x2)
+        .def_property_readonly("n_2x1", &PyLayout::n_2x1)
+        .def_property_readonly("n_2x2", &PyLayout::n_2x2) // TODO: return `1` directly
+
+        .def_property_readonly("type_id", &PyLayout::type_id)
+        .def_property_readonly("pattern_id", &PyLayout::pattern_id)
+        .def_property_readonly("case_id", &PyLayout::case_id)
+        .def_property_readonly("toward", &PyLayout::toward)
+        .def_property_readonly("group", &PyLayout::group_info)
+        .def_property_readonly("case_info", &PyLayout::case_info)
 
         .def_static("check", py::overload_cast<uint64_t>(&PyLayout::check))
         .def_static("check", py::overload_cast<std::string_view>(&PyLayout::check));
diff --git a/src/core_ffi/python_ffi/include/py_ffi/cases.h b/src/core_ffi/python_ffi/include/py_ffi/cases.h
index 63dbae0..a78eb21 100644
--- a/src/core_ffi/python_ffi/include/py_ffi/cases.h
+++ b/src/core_ffi/python_ffi/include/py_ffi/cases.h
@@ -5,12 +5,12 @@
 #include <variant>
 #include <ranges/ranges.h>
 
-#include "py_ffi/layout.h"
-
 namespace klotski::ffi {
 
 using cases::RangesUnion;
 
+class PyLayout;
+
 class PyCasesIter {
 public:
     /// Construct from RangesUnion reference.
diff --git a/src/core_ffi/python_ffi/include/py_ffi/group.h b/src/core_ffi/python_ffi/include/py_ffi/group.h
index d96dd86..5b18d63 100644
--- a/src/core_ffi/python_ffi/include/py_ffi/group.h
+++ b/src/core_ffi/python_ffi/include/py_ffi/group.h
@@ -7,7 +7,6 @@
 #include <group/group.h>
 
 #include "py_ffi/cases.h"
-#include "py_ffi/layout.h"
 #include "py_ffi/short_code.h"
 
 namespace klotski::ffi {
@@ -39,6 +38,10 @@ public:
 
     [[nodiscard]] PyGroup to_horizontal_mirror() const;
 
+    static std::string repr(const PyGroup group) noexcept {
+        return std::format("<klotski.Group '{}'>", group.to_string()); // TODO: maybe add size info
+    }
+
 private:
     Group group_;
 };
diff --git a/src/core_ffi/python_ffi/include/py_ffi/layout.h b/src/core_ffi/python_ffi/include/py_ffi/layout.h
index 9630c61..98b808a 100644
--- a/src/core_ffi/python_ffi/include/py_ffi/layout.h
+++ b/src/core_ffi/python_ffi/include/py_ffi/layout.h
@@ -2,9 +2,11 @@
 
 #pragma once
 
-#include <mover/mover.h>
+#include <group/group.h>
+#include <mover/mover.h> // TODO: move to `.cc` file
 #include <common_code/common_code.h>
 
+#include "py_ffi/group.h"
 #include "py_ffi/short_code.h"
 
 // TODO: add `copy` and `pickle` support
@@ -20,6 +22,13 @@ enum class PyBlock : uint8_t {
     FILL = 0b111,
 };
 
+enum class PyToward : uint8_t { // TODO: from `Group::Toward` directly
+    A = 0,
+    B = 1,
+    C = 2,
+    D = 3,
+};
+
 class PyLayout {
 public:
     PyLayout() = delete;
@@ -70,6 +79,52 @@ public:
 
     // ------------------------------------------------------------------------------------- //
 
+    [[nodiscard]] uint8_t type_id() const noexcept {
+        return group::GroupUnion::from_common_code(code_).unwrap();
+    }
+
+    [[nodiscard]] uint16_t pattern_id() const noexcept {
+        return group_info().pattern_id();
+    }
+
+    [[nodiscard]] PyToward toward() const noexcept {
+        const auto group = group::GroupCases::obtain_group(code_);
+        return (PyToward)group.toward();
+    }
+
+    [[nodiscard]] PyGroup group_info() const noexcept {
+        const auto group = group::GroupCases::obtain_group(code_);
+        return std::bit_cast<PyGroup>(group);
+    }
+
+    [[nodiscard]] uint32_t case_id() const noexcept {
+        const auto info = group::GroupCases::obtain_info(code_);
+        return info.case_id();
+    }
+
+    [[nodiscard]] std::tuple<PyGroup, uint32_t> case_info() const noexcept {
+        const auto info = group::GroupCases::obtain_info(code_);
+        return std::make_tuple(std::bit_cast<PyGroup>(info.group()), info.case_id());
+    }
+
+    [[nodiscard]] uint8_t n_1x1() const noexcept {
+        return std::get<2>(group::BLOCK_NUM[type_id()]);
+    }
+
+    [[nodiscard]] uint8_t n_1x2() const noexcept {
+        return std::get<0>(group::BLOCK_NUM[type_id()]) - n_2x1();
+    }
+
+    [[nodiscard]] uint8_t n_2x1() const noexcept {
+        return std::get<1>(group::BLOCK_NUM[type_id()]);
+    }
+
+    [[nodiscard]] uint8_t n_2x2() const noexcept {
+        return 1;
+    }
+
+    // ------------------------------------------------------------------------------------- //
+
 private:
     codec::CommonCode code_;
 };
diff --git a/src/core_ffi/python_ffi/packing/src/klotski/__init__.py b/src/core_ffi/python_ffi/packing/src/klotski/__init__.py
index e7c8909..66995c8 100644
--- a/src/core_ffi/python_ffi/packing/src/klotski/__init__.py
+++ b/src/core_ffi/python_ffi/packing/src/klotski/__init__.py
@@ -1,3 +1,3 @@
-from ._klotski import Cases, CommonCode, FastCal, Group, GroupUnion, ShortCode
+from ._klotski import Cases, Layout, FastCal, Group, GroupUnion, ShortCode, Toward, Block
 
-__all__ = ["Cases", "CommonCode", "FastCal", "Group", "GroupUnion", "ShortCode"]
+__all__ = ['Cases', 'Layout', 'FastCal', 'Group', 'GroupUnion', 'ShortCode', 'Toward', 'Block']
diff --git a/src/core_ffi/python_ffi/wrapper/cases.cc b/src/core_ffi/python_ffi/wrapper/cases.cc
index f75b37f..3a8f260 100644
--- a/src/core_ffi/python_ffi/wrapper/cases.cc
+++ b/src/core_ffi/python_ffi/wrapper/cases.cc
@@ -2,6 +2,7 @@
 #include <pybind11/pybind11.h>
 
 #include "py_ffi/cases.h"
+#include "py_ffi/layout.h"
 
 namespace py = pybind11;
 
diff --git a/src/core_ffi/python_ffi/wrapper/group_union.cc b/src/core_ffi/python_ffi/wrapper/group_union.cc
index eac93ba..ca57f25 100644
--- a/src/core_ffi/python_ffi/wrapper/group_union.cc
+++ b/src/core_ffi/python_ffi/wrapper/group_union.cc
@@ -1,5 +1,6 @@
 #include "exception.h"
 #include "py_ffi/group.h"
+#include "py_ffi/layout.h"
 
 using klotski::codec::ShortCode;
 using klotski::codec::CommonCode;