Polyhedra

Dodecahedron: # of faces, # of vertices, # of edges, face shape

12, 12, 30, pentagon

Icosahedron: # of faces, # of vertices, # of edges, face shape

20, 12, 30, equilateral triangle

Tetrahedron: # of faces, # of vertices, # of edges, face shape

4, 4, 6, equilateral triangle

Cube: # of faces, # of vertices, # of edges, face shape

6, 8, 12, square

Octahedron: # of faces, # of vertices, # of edges, face shape

8, 6, 12, equilateral triangle

What is Euler's Formula?

Vertices - edges + faces = 2

Polyhedra is a greek word meaning

a 3D object where you connect polygons along straight edges

Why cant there be more than five platonic solids

because a polygon with 6 sides or more can't fit together because 3 shapes cannot fit into 1 vertex which is the minimum

What are the two reversible dualities?

cube-octahedron, icosahedron-dodecahedron

a _________ of a polyhedron is a flat surface formed by a polygon

face

a _________ is a flattened out 3D shape

net

a polyhedron is a __________ if all faces are congruent regular polygons and all faces meet at teach vertex in exactly the same way

platonic solid

a _________ is a 3D figure formed by regions shaped like polygons that share a common side

polyhedra

What are the five platonic solids?

regular tetrahedron, regular octahedron, regular icosahedron, regular cube, regular dodecahedron

an ________ of a polyhedron is the point at which three or more edges intersect

vertex or corner