Generated Mesh is partially rendered, but shown correctly in scene view

I generate a mesh by code. In the Scene and Game View, it is shown correctly, but when i look at the generated mesh in the inspector preview, only half the triangles are generated. The other ones are only visible on the other side, when i flip the preview around.

To explain, here are some screenshots:

Scene View

Game View

Inspector Preview

Inspector Preview flipped over

I also added a collision to my mesh. If i place a cube with gravity enabled over the mesh, it only collides with the triangles shown in picture #3.. This is also my main problem.

I think i have something with the triangles or the normals wrong, so here is my code.

     MeshFilter mf = GetComponent<MeshFilter>();
     Mesh mesh = new Mesh();
     mf.mesh = mesh;
     
     //Vertices
     Vector3[] verticies = new Vector3[]
     {
         new Vector3(0,0,0), 
         new Vector3(2,0,0), 
         new Vector3(0,0,3), 
         new Vector3(2,0,3),
         
         new Vector3(0,0,4), 
         new Vector3(2,0,4), 
         new Vector3(0,0,6), 
         new Vector3(2,0,6),
         
         new Vector3(0,0,7), 
         new Vector3(6,0,7), 
         new Vector3(0,0,9), 
         new Vector3(6,0,9),
         
         new Vector3(4,0,0), 
         new Vector3(6,0,0), 
         new Vector3(4,0,2), 
         new Vector3(6,0,2),
         
         new Vector3(5,0,2), 
         new Vector3(6,0,2), 
         new Vector3(5,0,4), 
         new Vector3(6,0,4),
         
         new Vector3(4,0,4), 
         new Vector3(6,0,4), 
         new Vector3(4,0,6), 
         new Vector3(6,0,6)
     };
     
     //Triangles
     int[] tri = new int[]
     {
         0,1,2,
         1,2,3,
         
         4,5,6,
         5,6,7,
         
         8,9,10,
         9,10,11,
         
         12,13,14,
         13,14,15,
         
         16,17,18,
         17,18,19,
         
         20,21,22,
         21,22,23
     };
     
     //Normals, to see the Object
     Vector3[] normals = new Vector3[]
     {
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward,
         -Vector3.forward
     };
     
     //UVs what is displayed
     Vector2[] uv = new Vector2[]
     {
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1),
         
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1),
         
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1),
         
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1),
         
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1),
         
         new Vector2(0,0),
         new Vector2(1,0),
         new Vector2(0,1),
         new Vector2(1,1)
     };
     
     //Assign Arrays to Object
     mesh.vertices    = verticies;
     mesh.triangles     = tri;
     mesh.normals    = normals;
     mesh.uv         = uv;
     
     MeshCollider mc = gameObject.AddComponent(typeof(MeshCollider)) as MeshCollider;
     mc.sharedMesh = mesh; // Give it your mesh 

I hope some of you can help me, i'd appretiate it!