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What is the Platonic Solid and How many are there and What are their names?
Answering your questions one at a time.1 - What is a platonic solid?A platonic solid is one with all faces congruent polygons, meaning that they all have the same number of sides, vertices and angle size.2 - How many are there?There are only and exactly five.3 - What are their names?TetrahedronCube (but when talking about Platonic solids, it is commonly referred to as a "hexahedron").OctahedronDodecahedronIcosahedronNote: These individual platonic solids can be identified by their unique Schlafli Symbol. This is demonstrated through the following:{p,q}p = Number of vertices at each faceq = Number of faces at each vertexSo for a dodecahedron, the Shlafli Symbol would be {5,3}, because a pentagon has five {5, or p} vertices, and at any individual vertex three {3, or q} faces meet.Understand? Great!
Is a polyhedron a cube?
A polyhedron is a solid with flat faces - a cube is just one of many different examples of regular polyhedra - otherwise known as platonic solids.
Why are there only five platonic solids?
Because 6 platonic solids would be too many, and 4 wouldn't be enough
What is a platonic solid and how many are there and what are their names?
A Platonic solid is the 3-D shape equivalent of a polygon: it is a three dimensional figure whose sides are congruent, regular polygons, with identical vertices. Unlike the 2-dimensional case (in which there are infinitely many polygons) there are only 5 Platonic solids: * The tetrahedron, which has 4 triangular sides. * The cube (or hexahedron), which has 6 square sides. * The octahedron, which has 8 triangular sides. * The dodecahedron, which has 12 pentagonal sides. * The icosahedron, which has 20 triangular sides. Here is how the 5 Platonic solids were found, and how we know there aren't any more: Think about the sum of the angles at a vertex (by the definition of a Platonic solid, all vertices are identical). In the plane, angles around a vertex add up to 360 degrees, but we don't want the vertex to lie flat - otherwise, we'd end up with a huge flat sheet instead of a polyhedron. We also want at least 3 polygons around a vertex, because otherwise the result will become a flat figure without volume. If the sides are triangles, we can have 3 triangles around a vertex (getting the tetrahedron), 4 triangles around a vertex (getting the octahedron), or 5 triangles around a vertex (getting the icosahedron). We can't have 6 or more, because then the sum of angles wouldn't be less than 360. If the sides are squares, we can have 3 squares around a vertex, getting the cube. 4 squares around a vertex would mean the sum of angles is 360, and 5 or more is even more impossible. Finally, we can take 3 pentagons around a vertex, getting the dodecahedron; more pentagons will give us an angle sum of over 360. We can't use any shapes with more than 6 sides, because their angles are larger and we can't even fit 3 around a vertex. Even 3 hexagons will give an angle sum of 360 degrees, and anything more than that is even worse.
How many names does a square have?
It has seven names
What is the Platonic Solid and How many are there and What are their names?
Answering your questions one at a time.1 - What is a platonic solid?A platonic solid is one with all faces congruent polygons, meaning that they all have the same number of sides, vertices and angle size.2 - How many are there?There are only and exactly five.3 - What are their names?TetrahedronCube (but when talking about Platonic solids, it is commonly referred to as a "hexahedron").OctahedronDodecahedronIcosahedronNote: These individual platonic solids can be identified by their unique Schlafli Symbol. This is demonstrated through the following:{p,q}p = Number of vertices at each faceq = Number of faces at each vertexSo for a dodecahedron, the Shlafli Symbol would be {5,3}, because a pentagon has five {5, or p} vertices, and at any individual vertex three {3, or q} faces meet.Understand? Great!
How many platonic solids are their?
There (not their) are 5 platonic solids.
How many edges does a platonic solids have?
There are different numbers on the different platonic solids.
Is a polyhedron a cube?
A polyhedron is a solid with flat faces - a cube is just one of many different examples of regular polyhedra - otherwise known as platonic solids.
Why does a Platonic solid look the same no matter which vertex you position at the top?
Oh, dude, it's like this Platonic solid is just super symmetrical, you know? So, no matter which way you flip it, it's gonna look the same. It's like that one friend who always has their good side in every picture, except in 3D.
Why are there only five platonic solids?
Because 6 platonic solids would be too many, and 4 wouldn't be enough
Why are they only five platonic solids?
Because 6 platonic solids would be too many, and 4 wouldn't be enough
A pyramid has how many faces and sides?
A rectangular pyramid has five faces. Sides are the same things as faces. A pyramid with a triangular base has 4 faces. This is the more common type of pyramid in mathematics, as it is a platonic solid.
What is a solid with two parallel and congruent bases?
There are many possible answers: Any one of the four larger Platonic solids (not the tetrahedron). In all cases, moving one of the faces laterally will still leave a solid which will beet the requirements : the cube (hexahedron) could become a rhombohedron. There are many more shapes with fewer symmetries.
How many regular 3d shapes are there?
There are five Platonic solids: Tetrahedron (or triangular pyramid): 4 triangular faces Cube: 6 square faces Octahedron: 8 triangular faces Dodecahedron: 12 pentagonal faces Icosahedron: 20 triangular faces. Although not a Platonic solid, some people consider a sphere to be a regular 3d shape.
How many faces does octahedron has?
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.It is a 3-dimensional cross polytope (shape).---Wikipedia
How many things can you list of solid?
Solids have a defined shape and volume. Some examples include ice, wood, metal, and plastic.
