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Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.
What makes a shape a Platonic solid?
A Platonic Solid is a 3D shape where: each face is the same regular polygon. the same number of polygons meet at each vertex (corner).
Why are there 5 Platonic solids?
So only one Platonic solid can be made from pentagons. STEP 4: Three regular hexagons just make a flat sheet. And shapes with more sides, like heptagons or octagons, can’t fit together to make the minimum three faces to make a corner. Therefore we can only make five Platonic solids.
Is there a sixth Platonic solid?
Meet the Hyper-Diamond! It’s the sixth Platonic Solid and it only works in the fourth dimension.
Does every Platonic solid have a dual?
Every Platonic solid has a corresponding dual polyhedron that can be found through a fairly easy process. The simplest way to create the dual polyhedron for a Platonic solid is by finding the midpoints of each of the faces, and then connecting these midpoints so that they become the vertices of the new dual polyhedon.
How do you identify a Platonic solid?
Platonic solids have polygonal faces that are similar in form, height, angles, and edges. All the faces are regular and congruent. Platonic shapes are convex polyhedrons. The same number of faces meet at each vertex.
Is the Earth a dodecahedron?
Earth has the shape of a hexahedron or cube (Timaeus 54e–55b). Although Plato does not mention the shape of these leather pieces, scholars agree that he is hinting at a dodecahedron, which is a polyhedron made of 12 regular pentagons (Fig. 17.2).
Is a soccer ball a regular solid?
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons.
Why are there no regular polyhedra with sides being regular hexagons?
You cannot make a polyhedron out of hexagons, septagons, or any larger regular polygon alone. The reason is because their angles are too big. If you try to fit three hexagons together meeting a vertex, they are forced to lie in the same plane because their three 120° angles add up to a full 360°.
Who discovered the dodecahedron?
When Hippasus of Metapontum (who is credited with discovering the dodecahedron) divulged the secret of the existence of the irrational, he was thrown in the river and drowned. Phi, expressed to about 20,000 places is printed to the surface in the painting.
What element is the dodecahedron?
The fifth, the dodecahedron, has pentagonal faces. Plato believed that the first four corresponded to the elements of which the Greeks thought the material world was composed: fire, air, water and earth. The dodecahedron, however, corresponded to quintessence, the element of the heavens.
What are the 5 regular polyhedra?
Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron. Pythagoras (c. 580–c. 500 bc) probably knew the tetrahedron, cube, and dodecahedron.
What is bigger than a dodecahedron?
In geometry, the rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
What makes Hexahedron different from other regular solids?
A hexahedron (plural: hexahedra) is any polyhedron with six faces. (Two polyhedra are “topologically distinct” if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.).
Which regular polyhedra are duals of each other?
Any polyhedron can be associated with a second (abstract, combinatorial, topological) dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.Dual Polyhedron. polyhedron dual tetrahedron tetrahedron.
What do you do after dodecahedron?
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively.
What is a Platonic solid for kids?
A platonic solid is a three dimensional shape. It has the following characteristics: Each face is built from the same type of polygons. There are the same number of polygons meeting at every corner of the shape.
Are all prisms Platonic solids?
No, not all prisms are platonic solids, but some are. By definition, a prism is a solid object that has flat faces and identical faces on each end.
Is the universe shaped like a dodecahedron?
New findings in 2003 reveal that the shape of the Universe is a Dodecahedron based on Phi. Like visible light from distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was in its infancy.
Why is the dodecahedron special?
While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner.
What does the dodecahedron represent?
The dodecahedron is said to represent the universe; while the other four Platonic solids represent earth, fire, water and air, the five elements.
Is a soccer ball a Platonic solid?
The Platonic solids give rise to generalized soccer balls by a procedure known as truncation. Suppose we take a sharp knife and slice off each of the corners of an icosahedron. At each of the 12 vertices of the icosahedron, five faces come together at a point. Mathematicians call it the truncated icosahedron.
Why does a soccer ball have 32 panels?
The ball’s classic construction with 32 panels means that the ball meets resistance at a later point in its trajectory through the air, thus retaining a steady, high speed over a longer period of time. This provides a stable and more predictable flight – highly valued by all soccer players.
Is a cube a Hexahedron?
A hexahedron is a polyhedron with six faces. The unique regular hexahedron is the cube.
