In two dimensions 6 triangles meet at a vertex. In 3-dimensions any number of triangles (greater than 2) can meet at a vertext - a pyramid with the base in the shape of an n-gon will have n triangles meeting at its apex.
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That shape is a unit equilateral triangular dipyramid, and it has 6 faces.
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Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.
5 triangles.
Tetrahedron 3 triangles meet at each vertex 4 Faces 4 Vertices 6 Edges Cube 3 squares meet at each vertex 6 Faces 8 Vertices 12 Edges Octahedron 4 triangles meet at each vertex 8 Faces 6 Vertices 12 Edges Dodecahedron 3 pentagons meet at each vertex 12 Faces 20 Vertices 30 Edges Icosahedron 5 triangles meet at each vertex 20 Faces 12 Vertices 30 Edges