diff --git a/src/core/data/tiles/tile_set.hpp b/src/core/data/tiles/tile_set.hpp
index d99575cc9..61e9001ba 100644
--- a/src/core/data/tiles/tile_set.hpp
+++ b/src/core/data/tiles/tile_set.hpp
@@ -6,9 +6,8 @@
 #include "core/def.hpp"
 #include "core/data/ndarray/ndarray_vector.hpp"
 
-#include <iostream>
 #include <array>
-#include <tuple>
+#include <utility>
 #include <string>
 
 namespace PHARE::core
@@ -19,7 +18,7 @@ class TileSet
 public:
     static auto constexpr dimension = Tile::dimension;
 
-    TileSet(Box<int, dimension> const& box, std::array<int, dimension> const& tile_size)
+    TileSet(Box<int, dimension> const& box, std::array<std::size_t, dimension> const& tile_size)
         : box_{box}
         , tile_size_{tile_size}
         , shape_{[&]() {
@@ -68,6 +67,12 @@ class TileSet
     NO_DISCARD auto& operator[](std::size_t i) { return tiles_[i]; }
     NO_DISCARD auto const& operator[](std::size_t i) const { return tiles_[i]; }
 
+    template<typename... Index>
+    NO_DISCARD auto& at(Index... indexes)
+    {
+        return cells_(indexes...);
+    }
+
 private:
     void consistent_tile_size_() const
     {
@@ -132,7 +137,7 @@ class TileSet
     }
 
 
-    //! bri
+    //! store the pointer to the tile associated with each cell
     void tag_cells_()
     {
         for (auto& tile : tiles_)
@@ -146,7 +151,7 @@ class TileSet
 
 
     Box<int, dimension> box_;
-    std::array<int, dimension> tile_size_;
+    std::array<std::size_t, dimension> tile_size_;
     std::array<int, dimension> shape_;
     std::vector<Tile> tiles_;
     NdArrayVector<dimension, Tile*> cells_;
diff --git a/tests/core/data/particles/test_particle_tiles.cpp b/tests/core/data/particles/test_particle_tiles.cpp
index d2373f600..99032226b 100644
--- a/tests/core/data/particles/test_particle_tiles.cpp
+++ b/tests/core/data/particles/test_particle_tiles.cpp
@@ -28,7 +28,7 @@ TYPED_TEST(ParticleTileTest, constructs)
 {
     constexpr auto dim = TypeParam::dimension;
     Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(50)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
+    auto const tile_size = PHARE::core::ConstArray<std::size_t, dim>(4);
     TileSet<TypeParam> particleTileSet{box, tile_size};
 }
 
diff --git a/tests/core/data/tiles/test_tile.cpp b/tests/core/data/tiles/test_tile.cpp
index e50ea6f7f..8890c7209 100644
--- a/tests/core/data/tiles/test_tile.cpp
+++ b/tests/core/data/tiles/test_tile.cpp
@@ -15,12 +15,54 @@ using namespace PHARE::core;
 
 
 template<typename TileSet>
-class TileTest : public ::testing::Test
+class TileTestBase
+{
+public:
+    static auto constexpr dimension = TileSet::dimension;
+
+    TileTestBase(Box<int, dimension> box_, std::array<std::size_t, dimension> const& tile_size)
+        : box{box_}
+        , tileSet{box, tile_size}
+    {
+    }
+
+    Box<int, dimension> box;
+    TileSet tileSet;
+};
+
+template<typename TileSet>
+class TileTestBoxShapeNotMultipleTileSize : public TileTestBase<TileSet>, public ::testing::Test
 {
 public:
-    TileTest() {}
+    TileTestBoxShapeNotMultipleTileSize()
+        : TileTestBase<TileSet>{
+              Box<int, TileSet::dimension>{ConstArray<int, TileSet::dimension>(0),
+                                           ConstArray<int, TileSet::dimension>(54)},
+              ConstArray<std::size_t, TileSet::dimension>(4)}
+    {
+    }
+};
+
+template<typename TileSet>
+class TileTestBoxShapeMultipleTileSize : public TileTestBase<TileSet>, public ::testing::Test
+{
+public:
+    TileTestBoxShapeMultipleTileSize()
+        : TileTestBase<TileSet>{
+              Box<int, TileSet::dimension>{ConstArray<int, TileSet::dimension>(0),
+                                           ConstArray<int, TileSet::dimension>(47)},
+              ConstArray<std::size_t, TileSet::dimension>(4)}
+    {
+    }
+};
+
+
+template<typename TileSet>
+class TileTest : public ::testing::Test
+{
 };
 
+
 template<std::size_t dim>
 class TileMock : public Box<int, dim>
 {
@@ -28,70 +70,52 @@ class TileMock : public Box<int, dim>
 
 using DimTiles = testing::Types<TileSet<TileMock<1>>, TileSet<TileMock<2>>, TileSet<TileMock<3>>>;
 
+TYPED_TEST_SUITE(TileTestBoxShapeNotMultipleTileSize, DimTiles);
+TYPED_TEST_SUITE(TileTestBoxShapeMultipleTileSize, DimTiles);
 TYPED_TEST_SUITE(TileTest, DimTiles);
 
-TYPED_TEST(TileTest, expectedNbrOfTilesPerDimToCoverTheBox)
-{
-    constexpr auto dim = TypeParam::dimension;
-    Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(50)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
-    TypeParam cs{box, tile_size};
 
-
-    auto const& shape = cs.shape();
-    for (auto i = 0u; i < dim; ++i)
-        EXPECT_EQ(shape[i], 13);
+TYPED_TEST(TileTestBoxShapeNotMultipleTileSize, expectedNbrOfTilesPerDimToCoverTheBox)
+{
+    auto const& shape = this->tileSet.shape();
+    for (auto i = 0u; i < this->dimension; ++i)
+        EXPECT_EQ(shape[i], 14);
 }
 
-TYPED_TEST(TileTest, cluserSetSizeIsCorrect)
+TYPED_TEST(TileTestBoxShapeMultipleTileSize, cluserSetSizeIsCorrect)
 {
-    constexpr auto dim = TypeParam::dimension;
-    Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(47)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
-    TypeParam cs{box, tile_size};
-
-    EXPECT_EQ(cs.size(), std::pow(12, dim));
+    EXPECT_EQ(this->tileSet.size(), std::pow(12, this->dimension));
 }
 
 
-TYPED_TEST(TileTest, totalTileSetSurfaceIsEqualToBoxSurface)
+TYPED_TEST(TileTestBoxShapeNotMultipleTileSize, totalTileSetSurfaceIsEqualToBoxSurface)
 {
-    constexpr auto dim = TypeParam::dimension;
-    Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(49)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
-    TypeParam cs{box, tile_size};
-
     auto surface = 0.;
-    for (auto i = 0u; i < cs.size(); ++i)
+    for (auto i = 0u; i < this->tileSet.size(); ++i)
     {
         auto current_surface = 1.;
-        for (auto d = 0u; d < dim; ++d)
+        for (auto d = 0u; d < this->dimension; ++d)
         {
-            auto l = (cs[i].upper[d] - cs[i].lower[d] + 1);
+            auto l = (this->tileSet[i].upper[d] - this->tileSet[i].lower[d] + 1);
             current_surface *= l;
         }
         surface += current_surface;
     }
-    EXPECT_EQ(surface, box.size());
+    EXPECT_EQ(surface, this->box.size());
 }
 
 
 
-TYPED_TEST(TileTest, tileHasNoOverlapWithOthers)
+TYPED_TEST(TileTestBoxShapeNotMultipleTileSize, tileHasNoOverlapWithOthers)
 {
-    constexpr auto dim = TypeParam::dimension;
-    Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(54)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
-    TypeParam cs{box, tile_size};
-
-    for (auto const& tile : cs)
+    for (auto const& tile : this->tileSet)
     {
-        for (auto const& other : cs)
+        for (auto const& other : this->tileSet)
         {
             if (&tile != &other)
             {
-                auto const box1 = Box<int, dim>{tile.lower, tile.upper};
-                auto const box2 = Box<int, dim>{other.lower, other.upper};
+                auto const box1 = Box<int, this->dimension>{tile.lower, tile.upper};
+                auto const box2 = Box<int, this->dimension>{other.lower, other.upper};
                 auto overlap    = box1 * box2;
                 EXPECT_FALSE(overlap.has_value());
             }
@@ -100,16 +124,13 @@ TYPED_TEST(TileTest, tileHasNoOverlapWithOthers)
 }
 
 
-TYPED_TEST(TileTest, retrieveTilesFromBoxOverlap)
+TYPED_TEST(TileTestBoxShapeNotMultipleTileSize, retrieveTilesFromBoxOverlap)
 {
-    constexpr auto dim = TypeParam::dimension;
-    Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(54)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(4);
-    TypeParam cs{box, tile_size};
-    Box<int, dim> selection_box{ConstArray<int, dim>(11), ConstArray<int, dim>(34)};
+    Box<int, this->dimension> selection_box{ConstArray<int, this->dimension>(11),
+                                            ConstArray<int, this->dimension>(34)};
 
-    auto expected_nbr = std::pow(7, dim);
-    auto overlapeds   = cs.export_overlaped_with(selection_box);
+    auto expected_nbr = std::pow(7, this->dimension);
+    auto overlapeds   = this->tileSet.export_overlaped_with(selection_box);
     EXPECT_EQ(overlapeds.size(), expected_nbr);
 
     auto completes   = 0.;
@@ -122,8 +143,8 @@ TYPED_TEST(TileTest, retrieveTilesFromBoxOverlap)
         else
             ++incompletes;
     }
-    EXPECT_EQ(completes, std::pow(5, dim));
-    EXPECT_EQ(incompletes, std::pow(7, dim) - std::pow(5, dim));
+    EXPECT_EQ(completes, std::pow(5, this->dimension));
+    EXPECT_EQ(incompletes, std::pow(7, this->dimension) - std::pow(5, this->dimension));
 }
 
 
@@ -131,11 +152,26 @@ TYPED_TEST(TileTest, cannotCreateTileWithTileSizeBiggerThanBox)
 {
     constexpr auto dim = TypeParam::dimension;
     Box<int, dim> box{ConstArray<int, dim>(0), ConstArray<int, dim>(5)};
-    auto const tile_size = PHARE::core::ConstArray<int, dim>(7); // larger than box shape
+    auto const tile_size = PHARE::core::ConstArray<std::size_t, dim>(7); // larger than box shape
     EXPECT_THROW(std::make_unique<TypeParam>(box, tile_size), std::runtime_error);
 }
 
 
+TYPED_TEST(TileTestBoxShapeNotMultipleTileSize, canRetrieveTileFromCell)
+{
+    auto tile = [&]() {
+        if constexpr (this->dimension == 1)
+            return this->tileSet.at(13);
+        else if constexpr (this->dimension == 2)
+            return this->tileSet.at(13, 13);
+        else if constexpr (this->dimension == 3)
+            return this->tileSet.at(13, 13, 13);
+    }();
+    auto const expected_box = Box<int, this->dimension>{ConstArray<int, this->dimension>(12),
+                                                        ConstArray<int, this->dimension>(15)};
+    EXPECT_TRUE(*tile == expected_box);
+}
+
 
 
 int main(int argc, char** argv)