Is there any way to know where the vertices of a tile are?

I have succeeded in obtaining a tile of a certain level and obtaining the x, y number of that tile.

  let tileLevels = [];
  let tiles = [];
  this.viewer.scene.globe._surface.forEachRenderedTile((tile) => {
    tileLevels.push(tile.level);
    if(tile.level>14){
      tiles.push(toString(tile.x),',',toString(tile.y));
    }
    console.log(`test | ${tile.level}, ${tile.x}, ${tile.y}`);
    // tile.rectangle are available
  });
  console.log(`test | levels : (${tileLevels.length}) [${tileLevels}]`);
  var ntile = Math.min.apply(null, tileLevels);

I plan to place characteristic symbol objects on the tiles with the smallest level, and gradually deepen building objects from the highest level tiles (exceeding level 14 in the code), which are the core.
The type of data you have is an index value that has nothing to do with a specific geographic range, making it difficult to infer latitude and longitude from an index.
I want to call the corresponding index in batch based on the tile information captured in the view.

Can I get the vertex of each tile? I want to get latitude and longitude through it.

The type of data you have is an index value that has nothing to do with a specific geographic range, making it difficult to infer latitude and longitude from an index.

3D Tiles Next supports implicit tiling schemes for this very reason.

Can I get the vertex of each tile? I want to get latitude and longitude through it.

Each tile can have many vertices. Are you looking for the center position? Or the bound of the tile?

tile.boundingSphere will provide you with the approximate bounds of the tile, and a center position.