Gap appears between two 2D hexagons sharing two vertices

Here are two scripts. Map is attached to a plane and instantiates objects of type Hex. The Hex.ToString() function prints vertices in (x,z) format because y is constant. Here is the result of the Hex.ToString() operations in advance:

Center: (0,0)

v1: (-6,0)

v2: (-3,5)

v3: (3,5)

v4: (6,0)

v5: (3,-5)

v6: (-3,-5)

Center: (-9,5)

v1: (-15,5)

v2: (-12,10)

v3: (-6,10)

v4: (-3,5)

v5: (-6,0)

v6: (-12,0)

The first hexagon's vertex v1 = the second hexagon's vertex v5 = (-6,0)

The first hexagon's vertex v2 = the second hexagon's vertex v4 = (-3,5)

The hexagons should overlap at a line drawn between the two shared vertices, however, they are spaced out. The size of these gaps also seems to scale with the radius of the hexagon.

 public class Map : MonoBehaviour 
 {
     private int radius = 6;
     void Awake() 
     {    
         Texture2D hexTexture = (Texture2D) Resources.Load ( "Hex" );
         
     
         Hex center = (Hex) this.gameObject.AddComponent ( "Hex" );
         center.Draw ( radius, 0, 0, hexTexture );
     
         Hex neighbor = (Hex) this.gameObject.AddComponent ( "Hex" );
         neighbor.Draw ( radius, -9, 5, hexTexture );
     }
 }

 public class Hex : MonoBehaviour
 {
     private const float y = 0.01f;
 
     public void Draw( int r, float x, float z, Texture2D hexTexture )
     {        
         gO = new GameObject();
         gO.transform.position = new Vector3( x, y, z );
         gO.name = ( "Hex (" + x.ToString () + "," + z.ToString () + ")" );
                          
         Vector3[] vertices = ComputeVertices( r, x, z );
         hexInfo = new HexInfo( r, x, z, vertices );
         
         Vector2 uvCenter = new Vector2( .5f, .5f );
         Vector2 uvV1 = new Vector2( 0, .5f );
         Vector2 uvV2 = new Vector2( .333f, 0 );
         Vector2 uvV3 = new Vector2( .666f, 0 );
         Vector2 uvV4 = new Vector2( 1, .5f );
         Vector2 uvV5 = new Vector2( .666f, 1 );
         Vector2 uvV6 = new Vector2( .333f, 1 );
         
         Vector2[] uv = { uvCenter, uvV1, uvV2, uvV3, uvV4, uvV5, uvV6 };
         
         int[] indeces = {
             6, 0, 5,
             5, 0, 4,
             4, 0, 3, 
             3, 0, 2,
             2, 0, 1,
             1, 0, 6,
         };
         
         Vector3[] normals = {
             Vector3.up,
             Vector3.up,
             Vector3.up,
             Vector3.up,
             Vector3.up,
             Vector3.up,
             Vector3.up
         };
         
         Mesh mesh = new Mesh();
         mesh.vertices = vertices;
         mesh.triangles = indeces;
         mesh.uv = uv;
         mesh.normals = normals;
         mesh.Optimize();
         
         MeshFilter meshFilter = (MeshFilter) gO.AddComponent( "MeshFilter" );
         meshFilter.mesh = mesh;
         
         MeshRenderer meshRenderer = (MeshRenderer) gO.AddComponent( "MeshRenderer" );
         meshRenderer.material.mainTexture = hexTexture;
         
         Debug.Log ( "Drew Hexagon: " + this.ToString () );
     }

 //   v2 -- v3
 //  /        \
 // /          \
 // v1    C    v4
 // \          /
 //  \        /
 //   v6 -- v5 

 
     //        v2
     //       /|\
     //    c / | \
     //     /  |b \  
      // v1 <-------Center
     //       a 
     //
     // All triangles in the hexagon have the properties of 
     // triangle (v1,v2,center), where a = c = radius
     //
     // Angle ab is a right angle whose line b bisects line a:
     // The x coordinate of v1 is the center's x coordinate - radius
     // The x coordinate of v4 is the center's x coordinate + radius
     // The x coordinate of v2 and v6 is the center's x value - 1/2 radius
     // The x coordinate of v3 and v5 is the center's x value + 1/2 radius
     //
     // line b's length is 1/2 of the hexagon's height H:
     // The z coordinate of v1 and v4 is the center's z coordinate
     // The z coordinate of v2 and v3 is the center's z value + b
     // The z coordinate of v6 and v5 is the center's z value - b
     private Vector3[] ComputeVertices( int r, float x, float z )
     {
         // Cast b to an integer to force rounding
         int b = (int) HexInfo.GetHeight ( r ) / 2;
         float halfRadius = r / 2;
         
         Vector3 center = new Vector3( x, y, z );
         Vector3 v1 = new Vector3( x - r, y, z );
         Vector3 v4 = new Vector3( x + r, y, z );
         
         Vector3 v2 = new Vector3( x - halfRadius, y, z + b );
         Vector3 v3 = new Vector3( x + halfRadius, y, z + b );
         Vector3 v5 = new Vector3( x + halfRadius, y, z - b );
         Vector3 v6 = new Vector3( x - halfRadius, y, z - b );
                         
         Vector3[] vertices = { center, v1, v2, v3, v4, v5, v6 };
         return vertices;
     }
 }