Can't render GameObject

When you use new GameObject() you have already instantiated a new empty gameObject, using Instantiate(gameObject) should make a second copy of this gameObject as it currently is so you should remove Instantiate(HexTile). It would also be a good idea to assign a new material to your renderer. However neither of these should make your gameObject invisible so I think the problem might be in another part of your code. Here is some code that works, try using it as a starting off point and see why your code does not create a visible object.

 GameObject gameObject=new GameObject("Triangle");
 
 MeshFilter filter=gameObject.AddComponent<MeshFilter>();
 Mesh mesh=new Mesh();
 mesh.vertices=new Vector3[]{
     new Vector3(0, 0),
     new Vector3(0, 1),
     new Vector3(1, 0),
 };
 mesh.triangles=new int[] { 
     0, 1, 2, 
 };
 mesh.uv=new Vector2[mesh.vertices.Length];
 mesh.RecalculateNormals();
 mesh.Optimize();
 filter.mesh=mesh;
 
 MeshRenderer renderer=gameObject.AddComponent<MeshRenderer>();
 renderer.material=new Material(Shader.Find("Diffuse"));
 renderer.material.color=Color.green;

Instead of coding this, you can just add a mesh renderer to the GameObject.

I can't see any differences between your code and mine. This is certainly frustrating. Could it be the way I am calling the function? My full code is as below (you can ignore the second region):

 using UnityEngine;
 using System.Collections;
 
 public class HexManager : MonoBehaviour {
 
     #region HexInfo
     
     public float HexUnitLength;
     
     [HideInInspector] public Vector3[] HexVertices;
     [HideInInspector] public Vector2[] HexUV;
     [HideInInspector] public int[] HexTriangles;
     
     public Texture HexTexture;
 
     [HideInInspector] public GameObject HexTile;
     
     void HexMeshSetup() {
         
         float floorLevel = 0;
         float HexSizeMult = HexUnitLength / Mathf.Sqrt(3);
 
         HexVertices = new Vector3[] {
             /*0*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(3+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(3+0.5)/6)))),
             /*1*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(2+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(2+0.5)/6)))),
             /*2*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(1+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(1+0.5)/6)))),
             /*3*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(0+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(0+0.5)/6)))),
             /*4*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(5+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(5+0.5)/6)))),
             /*5*/new Vector3((HexSizeMult * Mathf.Cos((float)(2*Mathf.PI*(4+0.5)/6))), floorLevel, (HexSizeMult * Mathf.Sin((float)(2*Mathf.PI*(4+0.5)/6))))
         };
         
         HexTriangles = new int[] {
             1,5,0,
             1,4,5,
             1,2,4,
             2,3,4
         };
         
         HexUV = new Vector2[] {
             new Vector2(0,0.25f),
             new Vector2(0,0.75f),
             new Vector2(0.5f,1),
             new Vector2(1,0.75f),
             new Vector2(1,0.25f),
             new Vector2(0.5f,0),
         };
 
         HexTile = new GameObject("Single Hex Tile");
 
         HexTile.transform.position = Vector3.zero;
         HexTile.transform.rotation = Quaternion.identity;
         HexTile.transform.localScale = Vector3.one;
 
         MeshFilter HexMeshFilter = HexTile.AddComponent<MeshFilter>();
         MeshRenderer HexMeshRenderer = HexTile.AddComponent<MeshRenderer>();
         
         Mesh HexMesh = new Mesh();
         HexMesh.vertices = HexVertices;
         HexMesh.triangles = HexTriangles;
         HexMesh.uv = HexUV;
 
         HexMesh.RecalculateNormals();
         
         HexMeshFilter.mesh = HexMesh;
         HexMeshRenderer.material.mainTexture = HexTexture;
 
     }
     
     #endregion
 
     #region GridGeneration
 
     public int GridWidth;
     public int GridHeight;
 
     public Vector3 C aalcInitPos() {
     
     // Position of the first tile placed will be the upper-left corner of the grid.
 
         Vector3 InitPos;
         InitPos = new Vector3(-HexUnitLength * GridWidth / 2f + HexUnitLength / 2,
                               0,
                               HexUnitLength * GridHeight / 2f - HexUnitLength / 2);
         
         return InitPos;
 
     }
 
     public Vector3 CalcWorldCoord(Vector2 GridPos) {
     
         Vector3 InitPos = CalcInitPos();
 
         float RowOffset = 0;
         if (GridPos.y % 2 != 0)
             RowOffset = HexUnitLength / 2;
         
         float x =  InitPos.x + RowOffset + GridPos.x * HexUnitLength;
         float z = InitPos.z - GridPos.y * HexUnitLength * 0.75f;
         return new Vector3(x, 0, z);
 
     }
 
     void CreateGrid() {
     
     //HexGrid will be a game object which is the parent of all the individual hex tiles
     
         GameObject HexGrid = new GameObject("HexGrid");
         
         for (float y = 0; y < GridHeight; y++) {
         
             for (float x = 0; x < GridWidth; x++) {
             
                 Vector2 GridPos = new Vector2(x, y);
                 GameObject HexClone = (GameObject)Instantiate(HexTile);
                 HexClone.transform.position = CalcWorldCoord(GridPos);
                 HexClone.transform.parent = HexGrid.transform;
             }
         }
     }
 
     #endregion
 
     #region Run
 
     void start() {
 
         HexMeshSetup();
         CreateGrid();
 
     }
 
     #endregion
 
 }