Disclaimer: this study guide was not created to replace Geometry your textbook and is for classroom or individual use only. Study Guides Study Page 1 of 2 Page v1.10.31.2011 , are formed by by formed are , lateral faces lateral Image Credit: Blue figures on this page by CK- rtguest, 2014, modified copyright Used under license from 12 Foundation. Shutterstock.com. edges of the polyhedron faces ; each edge joins exactly two vertices : square pyramid : octagonal prism vertices Right Right : A polyhedron where all the faces are congruent regular polygons. : A polyhedron where : The line segment where two lateral faces intersect. where two lateral : The line segment : A face that is not the base. : A face that is not has these properties: This guide was created by Nicole Crawford, Jane Li, Amy Shen, and Zachary Shen, and Zachary Jane Li, Amy Nicole Crawford, created by This guide was learn more about the student authors, http://www.ck12.org/ Wilson. To about/ck-12-interns/. (plural, polyhedra): A three-dimensional figure made up with polygon faces. with polygon A three-dimensional figure made up polyhedra): (plural, (plural, vertices): The point where two edges intersect. The point vertices): (plural, : A polyhedron with one base and triangular sides meeting at a common vertex. : hexagonal pyramid : hexagonal pyramid : triangular prism : The line segment where two faces intersect. : The line segment : A polygon in a polyhedron. : A polygon : A polyhedron with two parallel, congruent bases. The other faces, also called also faces, other The bases. congruent with two parallel, polyhedron A : Left Left Can be convex or concave Can be convex 3-dimensional • • olyhedra Lateral Face Lateral Edge connecting the corresponding vertices of the bases. connecting the corresponding vertices Pyramid Prism 7. 2. Made of only flat polygons, called the called 2. Made of only flat polygons, faces join together along segments called 3. Polygon 4. Each edge joins exactly two faces 5. Edges meet in points called vertices 6. There are no gaps between edges or 1. polyhedron Classifying Polyhedra Big Picture Key Terms • • Two common types of polyhedra include prisms and pyramids. Prisms and pyramids are named by their bases. are named by Prisms and pyramids include prisms and pyramids. of polyhedra common types Two Regular Polyhedron A Polyhedron Face Edge Vertex The 2-dimensional shapes of a polygon can be applied in a 3-dimensional figure. Such characteristics define polyhedra. polyhedra. define characteristics Such figure. 3-dimensional a in applied be can polygon a of shapes 2-dimensional The shapes. complex can include some very terms and general is a very Polyhedron P Geometry Named aftertheGreekphilosopherPlato, thefive regularpolyhedra are: Platonic Solids A If afiguredoesnotsatisfy Euler’s formula,thefigureisnotapolyhedron. This formulacanbeusedtofindthenumberof vertices ( P Page 2of 2 A polyhedronissemi-regularifallofitsfacesareregularpoly • Regular Polyhedra Euler’s FormulaforPolyhedra Notes Semi-Regular Polyhedra regular polyhedron 5. 4. regulardodecahedron:12-facedpolyhedronwhereallthefacesarepentagons 3. regularoctahedron:8-facedpolyhedronwhereallthefacesareequilateral triangles 2. cube:6-facedpolyhedronwhereallthefacesaresquares 1. 4. The 3. Thefigurehasnogapsorholes 2. SatisfiesEuler’s formulaforthenumberof vertices, faces,andedges 1. Allf Semi-regular polyhedra oftenhave twodifferentkindsoffaces,bothwhichareregularpolygons. olyhedra • regular icosahedron:20-facedpolyhedronwhereallthefacesareequilateral triangles regular tetrahedron: 4-facedpolyhedronwhereallthefacesareequilateral triangles Prisms witharegularpolygon baseareoneexampleofsemi-regularpolyhedron. figureisconvex (hasnoindentations) aces arecongruentregularpolygons F +V=E 2 hasthefollowingcharacteristics:

cont . V ), faces( gons andsatisfiesEuler’s formula. F ), oredges( E ) onapolyhedron: