Week 9 Flashcards
Planar regions
Made up of points inside a closed two-dimensional (flat) surface (face of polyhedra)
Polyhedra
Closed 3D shapes with polygonal faces (planar regions)
Face of polyhedra
Planar regions
Vertices/vertex
Corner points of a shape
Edges
Line segments where two faces meet; sides of the faces
Nets
Unfolded versions of a 3D shape
Pyramids
Polyhedron with one face being any sort of polygonal region (often called the base) and with all the other faces being triangular regions with one vertex in common
Regular pyramid
Base is shaped like a regular polygon and lateral faces are all congruent
Lateral edges of pyramid or prism
Edges not on the base of a pyramid or prism
Lateral faces of pyramid or prism
Faces that are not the base of the pyramid or prism
What shapes have bases?
Prism or pyramid
Prism
A polyhedron with two faces (called bases) that are parallel and congruent and whose other faces (lateral faces) are parallelogram regions (or special parallelograms such as rectangular ones) formed by joining corresponding vertices of the bases
Right prism
Lateral edges (ones not on the bases) are perpendicular to the edges at the bases
Oblique prism
Lateral edges are not perpendicular to the base edges
Oblique pyramid
Lateral edges are not all the same length
Apex of the pyramid
Vertex that is not on the base (also called vertex of the pyramid)
Euler’s formula
V + F = E + 2
where V is the number of vertices of a given polyhedron, F is the number of faces, and E is the number of edges
Representation
A way of communicating or thinking about something; in geometry, a drawing, model, net, word, or equation
Hidden edges
An edge in a drawing of a three-dimensional shape that cannot be seen from the viewpoint of the drawer; it is often indicated by dashed or lighter marks
Congruence
The quality whereby two figures have the same size and shape; shapes related by congruence are congruent shapes
Congruent shapes
Shapes related by congruence
Regular polyhedron
A polyhedron whose faces are all the same regular polygonal regions and have the same arrangement at each vertex. Also called Platonic solids.
Platonic solids
Another name for regular polyhedron - polyhedron whose faces are all the same regular polygonal regions and have the same arrangement at each vertex
Convex regular polyhedra
Interior angles of the polygons meeting at a vertex must add to less than 360 degrees
Regular tetrahedron
Four faces, each an equilateral triangular region (pyramid with 3 sides)
Regular hexahedron
Six faces, each a square region (cube)
Regular octahedron
Eight faces, each an equilateral triangular region (sort of like a 3D diamond)
Regular dodecahedron
Dodeca (12) has 12 pentagonal faces
Regular icosahedron
Icosa (20) has 20 triangular faces
Concave polyhedron
A polyhedron with a concave face, a polygonal face with an interior reflex angle (shape caves in)
Convex polyhedron
A polyhedron with only convex polygonal faces
Mantle
Goes around the shape, ie. in a prism it is made up of the lateral faces, in a cylinder it is the part that wraps around
Who is credited with discovering some regular convex polyhedra?
Pythagoras
What is the golden ratio
A ratio between two numbers that equals approximately 1.618
