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What platonic solid has pentagons for faces?
The platonic solid that has pentagons for faces is the dodecahedron. It consists of 12 regular pentagonal faces, 20 vertices, and 30 edges. The dodecahedron is one of the five Platonic solids, which are characterized by their faces being congruent regular polygons meeting at each vertex.
What are the three type of polygons that can be a platonic solid?
Equilateral triangles, squares, regular pentagons.
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.
Why can a regular hexagon not be the face of a platonic solid?
Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.
Why is there a platonic solids whose faces are hexagon?
There are no Platonic solids with hexagonal faces because of the geometric constraints related to the angles of regular polygons. A Platonic solid is defined as a three-dimensional shape with identical faces that are regular polygons, and the angles of hexagons do not allow for a convex arrangement that meets the required conditions for a solid. Specifically, the internal angles of a hexagon (120 degrees) are too large to fit together at a vertex in three-dimensional space without overlapping or creating a non-convex shape. Thus, Platonic solids can only be formed from triangles, squares, and pentagons.
What platonic solid has pentagons for faces?
The platonic solid that has pentagons for faces is the dodecahedron. It consists of 12 regular pentagonal faces, 20 vertices, and 30 edges. The dodecahedron is one of the five Platonic solids, which are characterized by their faces being congruent regular polygons meeting at each vertex.
Other than squares the polygons that can be the face of a Platonic solid are and?
equilateral triangles and regular pentagons
What solid has 12 flat faces?
Twelve regular pentagons comprise the faces of a dodecahedron.
What are the three type of polygons that can be a platonic solid?
Equilateral triangles, squares, regular pentagons.
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.
What are the three types of polygons that can be faces of a platonic solid?
triangles, squares and pentagons.
Why can a regular hexagon not be the face of a platonic solid?
Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.
How mwny face a dodecahedron have?
a dodecahedron is a regular geometric solid, it has 12 pentagons as faces, 30 vertices and 30 edges
What is the maximum number of equilateral triangles that can come together at each vertex of a solid?
10
How many faces does football have?
32 12 regular pentagons and 20 regular hexagons. the solid structure is called truncated icosahedron. the rotational group of a soccer ball is isomorphic to A5..
What is the least number of equilateral triangles that can come together at each vertex to form a solid?
Four, in order to form a tetrahedron; this is alos the simplest possible 3-dimensional object constructed of regular polygons.
How many pentagons to make a 3d pentagon?
If you are thinking of a solid with pentagonal faces, a dodecahedron, there are twelve pentagons
