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Harlan SanchezBS-ECE 3

i. ALPHABET OF LINES

FIG.

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FIG.

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Cuboid

Cuboid is a solid figurebounded by six faces,

forming a convexpolyhedron. In the more

general definition of acuboid, the only additional

requirement is that these sixfaces each be a

quadrilateral, and that theundirected graph formed by

the vertices and edges of thepolyhedron should be

isomorphic to the graph of acube [6].

Pentagonal

Pyramid

Pentagonal pyramid is apyramid with a pentagonalbase upon which is erected

five triangular faces thatmeet at a point (the vertex)

[7].

TriangularPyramid

Triangular bipyramid (ordipyramid) is the first in theinfinite set of face-transitivebipyramids. It is the dual of the triangular prism with 6isosceles triangle faces [8].

QuadrilateralFrustum

Quadrilateral frustum is aapex-truncated quadrilateralpyramid. It has a square fora base, a square for a top,

and sloping sides [9].

Cube

Cube is a three-dimensional

solid object bounded by sixsquare faces, facets or sides,with three meeting at each

vertex [10].

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Octahedron

Octahedron is a polyhedronwith eight faces. A regular

octahedron is a Platonic solidcomposed of eight

equilateral triangles, four of which meet at each vertex

[11

Dodecahedron

Dodecahedron is anypolyhedron with twelve flatfaces, with three meeting at

each vertex [12].

Icosahedron

Icosahedrons is a regularpolyhedron with 20 identicalequilateral triangular faces,

30 edges and 12 vertices. Ithas five triangular facesmeeting at each vertex [13].

Icosidodecahedron Number of faces: 32 Number of edges: 60

Number of vertices: 30

TruncatedTetrahedron Number of faces: 8

Number of edges: 18 Num ber of vertices: 12

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TruncatedOctahedron Number of faces: 14

Number of edges: 36 Number of vertices: 24

Truncated Cube Number of faces: 14 Number of edges: 36

Number of vertices: 24

Rhombicuboctahedron Number of faces: 26

Number of edges: 48 Number of vertices: 24

TruncatedCuboctahedron Number of faces: 26

Number of edges: 72 Number of vertices: 48

TruncatedIcosidodecahedron Number of faces: 62

Number of edges: 180 Number of vertices: 120

Snub Cube Number of faces: 38 Number of edges: 60

Number of vertices: 24

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Snub Dodecahedron Number of faces: 92

Number of edges: 150 Number of vertices: 60

TruncatedIcosahedron Number of faces: 32

Number of edges: 90 Number of vertices: 60

TruncatedDodecahedron Number of faces: 32

Number of edges: 90 Number of vertices: 60

Rhombicosidodecahedron Number of faces: 62

Number of edges: 120 Number of vertices: 60

Cuboctahedron Number of faces: 14 Number of edges: 24

Number of vertices: 12

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Hexagonal Pyramid Number of faces: 7

Number of edges: 12 Number of vertices: 7

Dodecagonal Pyramid Number of faces: 13 Number of edges: 24

Number of vertices: 13

Square Pyramid

Number of faces: 5 Number of edges: 8 Number of vertices: 5

Triangular Pyramid Number of faces: 4 Number of edges: 6

Number of vertices: 4

Octagonal Pyramid Number of faces: 9

Number of edges: 16 Number of vertices: 9

Triangular Prism Number of faces: 5 Number of edges: 9

Number of vertices: 6

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Pentagonal Prism Number of faces: 7

Number of edges: 15 Number of vertices: 10

Hexagonal Prism Number of faces: 8

Number of edges: 18 Number of vertices: 12

Heptagonal Prism Number of faces: 9

Number of edges: 21 Number of vertices: 14

Octagonal Prism Number of faces: 10 Number of edges: 24

Number of vertices: 16

Enneagonal Prism

Number of faces: 11 Number of edges: 27

Number of vertices: 18

Decagonal Prism

Number of faces: 12 Number of edges: 30 Number of vertices: 20

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Hendecagonal Prism Number of faces: 13 Number of edges: 33

Number of vertices: 22

Dodecagonal Prism

Number of faces: 14 Number of edges: 36

Number of vertices: 24

Dodecadodecahedron

Number of faces: 24 Number of edges: 60

Number of vertices: 30

PentagonalHexecontahedron Number of faces: 60

Number of edges: 150 Number of vertices: 92

PentagonalIcositetrahedron Number of faces: 24

Number of edges: 60 Number of vertices: 38

SquareTrapezohedron Number of faces: 8

Number of edges: 16 Number of vertices: 10

Decahedron Number of faces: 10 Number of edges: 20

Number of vertices: 12

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RhombicDodecahedron Number of faces: 12

Number of edges: 24 Number of vertices: 14

IsoscelesDodecahedron

Number of faces: 12 Number of edges: 18 Number of vertices: 8

Hexakaidecahedron

Number of faces: 16 Number of edges: 24

Number of vertices: 10

Isosceles Icosahedron Number of faces: 20 Number of edges: 30

Number of vertices: 12

Tetracontahedron Number of faces: 40 Number of edges: 60

Number of vertices: 22

Hecatohedron Number of faces: 100

Number of edges: 150 Number of vertices: 52

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Obelisk Number of faces: 9

Number of edges: 16 Number of vertices: 9

DecagonalDipyramidal

Antiprism Number of faces: 40 Number of edges: 60

Number of vertices: 22

Pentagonal-pentagrammic Shape

Number of faces: 17 Number of edges: 30

Number of vertices: 15

Hebdomicontadissaedron Number of faces: 72

Number of edges: 132 Number of vertices: 62

Hectohexecontadihedron

Number of faces: 162 Number of edges: 306

Number of vertices: 146

Faceted Oloid Number of faces: 40 Number of edges: 80

Number of vertices: 42

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iii. 2D GEOMETRIC FIGURES

1. Convex polygon is a simple polygon whose interior is a convex set [14].

2. Concave polygon will always have an interiorangle with a measure that is greater than 180degrees. A simple polygon that is not convex is

called concave [15].

3. Constructible polygon is a regular polygon thatcan be constructed with compass andstraightedge [16].

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4. circumscribed circle or circumcircle of apolygon is a circle which passes through all thevertices of the polygon [17].

5. equiangular polygon is a polygon whose vertexangles are equal. If the lengths of the sides are alsoequal then it is a regular polygon [18].

6. equilateral polygon is a polygon which has all sides of the same length [19].

7. regular polygon is a polygon that is equiangular (all angles are equal inmeasure) and equilateral (all sides have the same length) [20].

TYPES OF REGULAR POLYGON

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Note: The number enclosed in brackets is the number of sides of a regularpolygon.

8. Penrose tiling is a non-periodic tiling generated by anaperiodic set of prototiles [21].

9. Digon is a polygon with two sides (edges) and two vertices. It isdegenerate in a Euclidean space, but may be non-degenerate in aspherical space [22].

10. triangle is one of the basic shapes of geometry: a polygon withthree corners or vertices and three sides or edges which areline segments [23]

11. quadrilateral is a polygon with four sides (or 'edges') andfour vertices or corners [24] .

12. pentagon is any five-sided polygon [25].

13. hexagon is a polygon with six edges and six vertices. The total of the internal angles of any hexagon is 720 degrees [26].

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14. heptagon is a polygon with seven sides and seven angles [27].

15. octagon is a polygon that has eight sides [28].

16. nonagon is a nine-sided polygon [29].

17. decagon is any polygon with ten sides and ten angles, andusually refers to a regular decagon, having all sides of equallength and each internal angle equal to 144° [30].

18. hendecagon is an 11-sided polygon [31].

19. dodecagon is any polygon with twelve sidesand twelve angles [32].

20. hexadecagon (sometimes called a hexakaidecagon) isa polygon with 16 sides and 16 vertices [33].

21. icosagon is a twenty-sided polygon. The sum of anyicosagon's interior angles is 3240 degrees [34].

22. star polygon is a self-intersecting, equilateral equiangularpolygon, created by connecting one vertex of a simple,regular, p -sided polygon to another, non-adjacent vertex and

continuing the process until the original vertex is reached again [35].

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23. annulus is a ring-shaped geometric figure, or more generally, a termused to name a ring-shaped object. Or, it is the area between twoconcentric circles [36].

24. arbelos is a plane region bounded by asemicircle of diameter 1, connected tosemicircles of diameters r and (1 − r ), all orientedthe same way and sharing a common baseline

[37].

25. circle is a simple shape of Euclidean geometry consisting of the set of points in a plane that are a given distance from a given point,the centre [38].

26. circular sector or circle sector , is theportion of a disk enclosed by two radii and an arc, wherethe smaller area is known as the minor sector and thelarger being the major sector [39].

27. circular segment (also Meglio's area ) is anarea of a circle informally defined as an area which is"cut off" from the rest of the circle by a secant or achord [40].

28. crescent is generally the shape produced when a circular disk has asegment of another circle removed from its edge, so that whatremains is a shape enclosed by two circular arcs of different

diameters which intersect at two points[41].

29. ellipse is a plane curve that results from theintersection of a cone by a plane in a way thatproduces a closed curve [42].

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30. lemniscate refers to any of several figure-eight or

∞ shaped curves [43].

31. lune is an area on a sphere bounded by two half great circles[44].

32. oval or ovoid is any curve resembling an egg or anellipse, but not an ellipse [45].

33. Reuleaux triangle is, apart from the trivial case of thecircle, the simplest and best known Reuleaux

polygon, a curve of constant width [46].

34. vesica piscis is a shape that is the intersection of twocircles with the same radius, intersecting in such a waythat the center of each circle lies on the circumference of the other [47].

35. salinon is a geometrical figure that consists of foursemicircles [48].

36. semicircle is a two-dimensional geometric shapethat forms half of a circle. Being half of a circle's360°, the arc of a semicircle always measures 180°or a half turn [49].

37. sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball [50].

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38. Archimedean spiral (also known as the arithmeticspiral ) is a spiral named after the 3rd century BC

Greek mathematician Archimedes [51].

39. astroid is a particular type of curve: ahypocycloid with four cusps. Astroids are also superellipses[52].

40. deltoid , also known as a tricuspoid or Steinercurve , is a hypocycloid of three cusps. In other words, it is

the roulette created by a point on the circumference of acircle as it rolls without slipping along the inside of a circlewith three times its radius [53].

41. tomahawk is a "tool" in geometry consisting of asemicircle and two line segments [54]

REFERENCES:

[1] Weisstein, Eric W., "Tetrahedron" from MathWorld

[2] http://www.uwgb.edu/dutchs/symmetry/poly4-7f.htm

[3] Oxford English Dictionary 1904; Webster's Second International 1947

[4] Weisstein, Eric W., "Rhombohedron" from MathWorld.

[5] Weisstein, Eric W., "Trapezohedron" from MathWorld.

[6] Robertson, Stewart Alexander (1984), Polytopes and Symmetry, CambridgeUniversity Press, p. 75, ISBN 9780521277396

[7] Eric W. Weisstein , Pentagonal pyramid ( Johnson solid ) at MathWorld .

[8] Weisstein, Eric W., "Dipyramid" from MathWorld.

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[9] hexahedron . http://wordnet.princeton.edu/. WordNet. Princeton University

[10] Weisstein, Eric W., "Cube" from MathWorld.

[11] Klein, Douglas J. (2002). "Resistance-Distance Sum Rules" (PDF). CroaticaChemica Acta 75 (2): 633–649. Retrieved 2006-09-30.

[12] Weisstein, Eric W., "Dodecahedron" from MathWorld.

[13] Weisstein, Eric W., "Icosahedron" from MathWorld.

[14] Weisstein, Eric W., "Convex polygon" from MathWorld.

[15] Weisstein, Eric W., "Concave polygon" from MathWorld.

[16] Fermat factoring status by Wilfrid Keller.

[17] Dörrie, Heinrich, 100 Great Problems of Elementary Mathematics , Dover,1965.

[18] Weisstein, Eric W., "Equiangular Polygon" from MathWorld.

[19] Dice of the Dimensions

[20] Weisstein, Eric W., "Regular polygon" from MathWorld.

[21] General references for this article include Gardner 1997, pp. 1–30,Grünbaum & Shephard 1987, pp. 520–548 & 558–579, and Senechal 1996,pp. 170–206.

[22] Weisstein, Eric W., "Digon" from MathWorld.

[23] Weisstein, Eric W., "Equilateral Triangle" from MathWorld.

[24] Weisstein, Eric W., "Quadrilateral" from MathWorld.

[25] Weisstein, Eric W., "Pentagon" from MathWorld.

[26] Weisstein, Eric W., "Hexagon" from MathWorld.

[27] Weisstein, Eric W., "Heptagon" from MathWorld.

[28] Shorter Oxford English Dictionary (6th ed.), Oxford University Press, 2007,ISBN 978-0-19-920687-2

[29] Weisstein, Eric W., "Nonagon" from MathWorld.

[30] Weisstein, Eric W., "Decagon" from MathWorld.

[31] Weisstein, Eric W., "Hendecagon" from MathWorld.

[32] Weisstein, Eric W., "Dodecagon" from MathWorld.

[33] Weisstein, Eric W., "Hexadecagon" from MathWorld.

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[34] Weisstein, Eric W., "Icosagon" from MathWorld.

[35] Coxeter, Harold Scott Macdonald (1973). Regular polytopes . Courier DoverPublications. ISBN 9780486614809.

[36] Annulus definition and properties

[37] Weisstein, Eric W., "Arbelos" from MathWorld.

[38] Johnson, Roger A., Advanced Euclidean Geometry , Dover Publ., 2007.

[39] Gerard, L. J. V. The Elements of Geometry, in Eight Books; or, First Step in Applied Logic , London, Longman's Green, Reader & Dyer, 1874. p. 285

[40] Weisstein, Eric W., "Circular segment" from MathWorld.

[41] dictionary.reference.com : crescent

[42] Charles D. Miller, Margaret L. Lial, David I. Schneider: Fundamentals of College Algebra . 3rd Edition Scott Foresman/Little 1990. ISBN 0-673-38638-4,page 381

[43] J. Dennis Lawrence (1972). A catalog of special plane curves . DoverPublications. p. 124. ISBN 0-486-60288-5.

[46] The Five Squarable Lunes at MathPages

[45] "Oblong". Oxford English Dictionary . 1933

[46] Ein Wankel-Rotor ist kein Reuleux-Dreieck! German Translation A Wankel-Rotor is not a Reuleux-Triangle!

[47] Ein Wankel-Rotor ist kein Reuleux-Dreieck! German Translation A Wankel-Rotor is not a Reuleux-Triangle!

[48] Weisstein, Eric W.. ""Salinon." From MathWorld--A Wolfram Web Resource".Retrieved 2008-04-14.

[49] Euclid's Elements, Book VI, Proposition 13

[50] Pages 141, 149. E.J. Borowski, J.M. Borwein. Collins Dictionary of Mathematics . ISBN 0-00-434347-6.

[51] Sakata, Hirotsugu and Masayuki Okuda. "Fluid compressing device havingcoaxial spiral members". Retrieved 2006-11-25.

[52] J. Dennis Lawrence (1972). A catalog of special plane curves . DoverPublications. pp. 4–5,34–35,173–174. ISBN 0-486-60288-5.

[53] Weisstein, Eric W. "Deltoid." From MathWorld--A Wolfram Web Resource.http://mathworld.wolfram.com/Deltoid.html

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[54] MathWorld/Wolfram

Fig. 1:http://www.tpub.com/content/aviation/14018/css/14018_113.htm

Fig. 2:http://www.umasd.org/1333108571029370/lib/1333108571029370/The_Alphabet_of_Lines.pdf

External links:

http://www.korthalsaltes.com/model.php?name_en=oblique%20pentagonal%20prism