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A polyhedron whose faces are identical regular polygons?
Platonic solids.
How is a hexagonal pyramid a polyhedron?
A polyhedron is a simply connected 3-dimensional shape whose faces are all regular polygons. A hexagonal pyramid is a special case in which one face is a hexagon and six faces are triangles.
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 is the perimeter of a hexagon whose sides all equal?
n8?
A square whose sides measures ten centimeter can it fit in a regular hexagon?
Yes.. depending on the size of the hexagon's sides
A polyhedron whose faces are identical regular polygons?
Platonic solids.
What are the Platonic Solids and what do they look like?
The Modern Five Platonics are ( quite different than the originals known to Plato and Kepler, are in art classes: Sphere, cube, cone, cylinder, and Pyramid. Tetrahedron is another word for the last-named solid. it was a virtual connundrum in art classes that they were basic, required material and the theory was nobody could draw in perspective without this background. Jon Gnagy among others pushed the 5 Platonic solids in his art courses on TV. of course if one is drawing monuments, it is obvious.They were the type of thing that was popular with teachers not so popular with students.
What is meant by the word face in terms of platonic solid?
A platonic solid is a special kind of polyhedron. A polyhedron is a 3-D figure whose faces are polygons.In a platonic solid all faces are identical regular polygons. A polyhedron has faces, edges, and vertices. The numbers of each are related by Euler's formula, V+F=E+2
What makes a solid a regular platonic solid?
A Platonic solid is a solid all of whose face are regular and congruent polygons.There are five of these:A Tetrahedron. Four faces, each an equilateral triangle.Ad InfoA Hexahedron (Cube). Six faces, each a square.An Octahedron. Eight faces, each an equilateral triangle.A Dodecahedron. Twelve faces, each a regular pentagon.An Icosahedron. Twenty faces, each an equilateral triangle.
What do two tetrahedrons joined face to face make?
A regular triangular dipyramid. It is one of the 92 "Johnson solids". Those are the convex polyhedra whose faces are regular polygons, but do not belong to either of the two sets of highly symmetric polyhedra (the Platonic and the Archimedean), or to the perhaps less interesting two infinite families of prisms and antiprisms.
How is a hexagonal pyramid a polyhedron?
A polyhedron is a simply connected 3-dimensional shape whose faces are all regular polygons. A hexagonal pyramid is a special case in which one face is a hexagon and six faces are triangles.
What is equilaterlal hexagon?
It is a hexagon whose sides are all the same length. It need not be a regular hexagon.
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 is the perimeter of a hexagon whose sides all equal?
n8?
A square whose sides measures ten centimeter can it fit in a regular hexagon?
Yes.. depending on the size of the hexagon's sides
What is the perimeter of a regular hexagon whose sides are 52 cm?
312cm
What is the difference between a polyhedron and a regular polyhedron?
A Polyhedron is a closed plane figure whose faces are portions of planes. Prisms and pyramids are examples of Polyhedron's. While a Regular Polyhedron is a Polyhedron whose facces are all regular Polygons and whose Vertices are all alike. There are only five Regular Polyhedron's: Tetahedron , Octahedron , Icosahedron , Hexahedron , and Dodecahedron .To clarify, there are five known Platonic Solids: regular polyhedrons which are convex on all their vertices.The tetrahedron is also known as the triangular pyramid: a regular one has an identical equilateral triangle for each of its four faces. This is the one Platonic solid which is self-dual, as each face has three sides and each vertex joins three edges.The regular hexahedron is better known as the cube: each of its six faces is a square, and each vertex joins three edges. Its dual counterpart is the regular octahedron. In this case, each of its eight faces is three-sides (an equilateral triangle) and each vertex joins four edges. To picture the octahedron, think two square pyramids mated on their square faces, leaving only the triangular faces.Finally, there is the regular dodecahedron (12 faces), which is composed of regular pentagons (five sides). Each vertex again joins three edges. Its dual counterpart is the regular icosahedron. It has 20 triangular faces, and each vertex joins five edges.
