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How faces at each vertex does a cuboid have?
A cuboid has 6 faces, with 3 faces meeting at each vertex.
When cube one of the (five) Platonic solids. Name the other Platonic solids and describe the characteristics of each. How many faces does it have What shape are the faces How many faces come together?
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
How many regular triangles meet at each vertex?
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.
What are regular and irregular solids?
A regular solid is also called a platonic solid. It is a solid whose faces are identical regular polygons. There are 5 such solids. There are only 5 of them because a regular solid has 3, 4 or 5 regular polygons meeting at a vertex. If you look at the maximum number of angles you can see why there are exactly 5 platonic solids. The 5 platonic solid are: Tetrahedron where 3 triangles meet at each vertex, the octahedron where 4 meet at each vertex and the last one made of triangles is the icosahedrons which 5 triangles at each vertex, the cube which has 3 squares meeting at each vertex, and lastly the dodecahedron which is made up of regular pentagons with 3 meet at each vertex. In each case, you can see that 5 is the most number of triangles since 6 would be 6 x 60 degrees >360, 4 squares would be 4 x 90=360, and pentagons have interior angles of 108 degrees so you have (3×108°=324°). Anything more than that is greater than or equal to 360 degrees so not possible. Furthermore, a hexagon has an interior angle of 120 degrees so you cannot have 3 meeting at a vertex. A very famous mathematician named Euler also has a formula for the number of faces and vertices which if F+V-E=2 and anything more than the 5 regular solids would violate Euler's formula which has been proven to be true. Solids that are not regular are irregular solids.
How many faces come together at each vertex of cube?
Three.
