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FF/polydraw/!PolyDraw/Docs/Glossary
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HELP/GLOSSARY information for PolyDraw and PolyNet 22 Jun 97
Names of Polyhedra
Polyhedra were first studied by people like Plato and Archimedes, so they
have names based on ancient Greek words. The names are made up of several
parts, depending on whether they refer to 2 or 3D objects, and the number of
sides or faces.
Part of
word meaning example
poly- many a 'polygon' is a 2D figure
-gon a plane figure, 2D a 'polygon' has many sides
-hedron a 3D solid
-hedra more than one 3D solid
tetra- 4 faces a 'tetrahedron' is a 3D solid
penta- 5 sides or faces with 4 faces
hexa- 6 sides or faces
octa- 8 sides or faces
deca- 10 sides or faces rhombi - a 4 sided polygon, with all
dodeca- 12 sides or faces sides equal but not all angles
icosa- 20 sides or faces
triaconta-30 sides or faces delta - a triangle, or 3 sided polygon
??? 60 sides or faces which looks like the Greek letter D
Antiprism
a polyhedron made with two opposite faces identical regular polygons,
with n sides, and the other faces made up of 2n equilateral triangles
Duals
2 polyhedra are duals if the vertices of one can be put into a one-to-one
correspondence with the centres of the faces of the other.
Archimedean or semi-regular solids
13 polyhedra made from more than one kind of regular polygon,
with all vertices equal.
5 are made by truncating the Platonic solids
2 are 'quasi-regular' with only 2 kinds of faces, each one entirely
surrounded by the other
2 are made by truncating the quasi-regular ones
2 rhombi-***
1 snub cube
1 snub dodecahedron
Compound
polyhedron made by combining 2 or more Platonic solids with the same centre
Congruent
identically equal
Convex polygon
one with all the angles between its edges less than 180 degrees
Convex polyhedron
one with all its dihedral angles less than 180 degrees
Deltahedron
has faces made only from triangles, usually equilateral
Dihedral angle
internal angle between 2 faces which meet along a common edge
Edge of a polyhedron
line where two faces meet
Entantiomorphic
a polyhedron which can exist in two forms, left and right handed,
for example, the snub cube
Face of a polyhedron
one of the polygons making up the surface of the polyhedron
Johnson solids
all convex polyhedra with faces which are regular polygons, excluding
the Platonic and Archimeadean solids and the infinite sets of prisms
and antiprisms.
Kepler/Poinsot solids
similar to Platonic solids but with star polygons as faces.
compounds made from a regular polygon and its dual stuck together so that
their edges bisect at right angles.
They are the Stella Octangula, the great icosahedron and the 3 stellations
of the dodecahedron
Net - see Planar Net
Planar Net - a plane shape which can be folded into a polyhedron.
A given polyhedron may have several different nets.
Platonic solids
The five made from convex regular polygons of the same kind,
with all vertices identical and all dihedral angles equal
Polygon
a plane figure bounded by straight edges and vertices
Polyhedron
a set of polygons enclosing a portion of 3D space
Prism
a polyhedron made with two opposite faces identical regular polygons,
with n sides and the other faces n squares
Pyramid
a polyhedron with a base and triangular faces all connecting the base
to a single point above it. The base is usually a regular polygon.
Regular polygon
one with all sides the same length, and the internal angles between all
the sides equal
Regular polyhedron
As defined by Plato these are solids made from equal regular polygons.
This is not sufficient for a truly regular solid because all the deltahedra
(made from equilateral triangles) satisfy the condition.
In addition we must require all the vertices to be identical.
Star polygon
one with equal length sides, but some angles at their vertices are
greater than 180 degrees, so they are not convex
Stellation
a process of extending sides of polygons, (or planes of polyhedra)
until they intersect to form another polyhedron
Uniform polyhedron
one with all the faces regular polygons, and all the vertices identical,
that is, each vertex has same number of faces of the same kind arranged
in the same order.
Vertex - point on a polyhedron where at least 3 edges meet
Wenninger
A polyhedron described in the book 'Polyhedron Models' by M.J.Wenninger
00000000 20 20 20 20 20 20 20 20 48 45 4c 50 2f 47 4c 4f | HELP/GLO| 00000010 53 53 41 52 59 20 69 6e 66 6f 72 6d 61 74 69 6f |SSARY informatio| 00000020 6e 20 66 6f 72 20 20 50 6f 6c 79 44 72 61 77 20 |n for PolyDraw | 00000030 61 6e 64 20 50 6f 6c 79 4e 65 74 20 20 32 32 20 |and PolyNet 22 | 00000040 4a 75 6e 20 39 37 0a 0a 4e 61 6d 65 73 20 6f 66 |Jun 97..Names of| 00000050 20 50 6f 6c 79 68 65 64 72 61 0a 0a 20 20 50 6f | Polyhedra.. Po| 00000060 6c 79 68 65 64 72 61 20 77 65 72 65 20 66 69 72 |lyhedra were fir| 00000070 73 74 20 73 74 75 64 69 65 64 20 62 79 20 70 65 |st studied by pe| 00000080 6f 70 6c 65 20 6c 69 6b 65 20 50 6c 61 74 6f 20 |ople like Plato | 00000090 61 6e 64 20 41 72 63 68 69 6d 65 64 65 73 2c 20 |and Archimedes, | 000000a0 73 6f 20 74 68 65 79 0a 68 61 76 65 20 6e 61 6d |so they.have nam| 000000b0 65 73 20 62 61 73 65 64 20 6f 6e 20 61 6e 63 69 |es based on anci| 000000c0 65 6e 74 20 47 72 65 65 6b 20 77 6f 72 64 73 2e |ent Greek words.| 000000d0 20 54 68 65 20 6e 61 6d 65 73 20 61 72 65 20 6d | The names are m| 000000e0 61 64 65 20 75 70 20 6f 66 20 73 65 76 65 72 61 |ade up of severa| 000000f0 6c 0a 70 61 72 74 73 2c 20 64 65 70 65 6e 64 69 |l.parts, dependi| 00000100 6e 67 20 6f 6e 20 77 68 65 74 68 65 72 20 74 68 |ng on whether th| 00000110 65 79 20 72 65 66 65 72 20 74 6f 20 32 20 6f 72 |ey refer to 2 or| 00000120 20 33 44 20 6f 62 6a 65 63 74 73 2c 20 61 6e 64 | 3D objects, and| 00000130 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 0a 73 | the number of.s| 00000140 69 64 65 73 20 6f 72 20 66 61 63 65 73 2e 0a 20 |ides or faces.. | 00000150 20 20 20 20 20 20 20 20 0a 20 20 50 61 72 74 20 | . Part | 00000160 6f 66 20 0a 20 20 20 77 6f 72 64 20 20 20 20 6d |of . word m| 00000170 65 61 6e 69 6e 67 20 20 20 20 20 20 20 20 20 20 |eaning | 00000180 20 20 20 20 20 20 20 20 20 20 20 65 78 61 6d 70 | examp| 00000190 6c 65 0a 0a 20 20 20 70 6f 6c 79 2d 20 20 20 20 |le.. poly- | 000001a0 6d 61 6e 79 20 20 20 20 20 20 20 20 20 20 20 20 |many | 000001b0 20 20 20 20 20 20 20 20 20 20 20 61 20 27 70 6f | a 'po| 000001c0 6c 79 67 6f 6e 27 20 69 73 20 61 20 32 44 20 66 |lygon' is a 2D f| 000001d0 69 67 75 72 65 0a 20 20 2d 67 6f 6e 20 20 20 20 |igure. -gon | 000001e0 20 61 20 70 6c 61 6e 65 20 66 69 67 75 72 65 2c | a plane figure,| 000001f0 20 32 44 20 20 20 20 20 20 20 20 20 20 61 20 27 | 2D a '| 00000200 70 6f 6c 79 67 6f 6e 27 20 68 61 73 20 6d 61 6e |polygon' has man| 00000210 79 20 73 69 64 65 73 0a 20 20 2d 68 65 64 72 6f |y sides. -hedro| 00000220 6e 20 20 61 20 33 44 20 73 6f 6c 69 64 0a 20 20 |n a 3D solid. | 00000230 2d 68 65 64 72 61 20 20 20 6d 6f 72 65 20 74 68 |-hedra more th| 00000240 61 6e 20 6f 6e 65 20 33 44 20 73 6f 6c 69 64 0a |an one 3D solid.| 00000250 0a 20 20 74 65 74 72 61 2d 20 20 20 20 34 20 66 |. tetra- 4 f| 00000260 61 63 65 73 20 20 20 20 20 20 20 20 20 20 20 20 |aces | 00000270 20 20 20 20 20 20 20 61 20 27 74 65 74 72 61 68 | a 'tetrah| 00000280 65 64 72 6f 6e 27 20 69 73 20 61 20 33 44 20 73 |edron' is a 3D s| 00000290 6f 6c 69 64 0a 20 20 70 65 6e 74 61 2d 20 20 20 |olid. penta- | 000002a0 20 35 20 73 69 64 65 73 20 6f 72 20 66 61 63 65 | 5 sides or face| 000002b0 73 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |s | 000002c0 20 20 20 20 20 20 20 20 20 20 20 77 69 74 68 20 | with | 000002d0 34 20 66 61 63 65 73 0a 20 20 68 65 78 61 2d 20 |4 faces. hexa- | 000002e0 20 20 20 20 36 20 73 69 64 65 73 20 6f 72 20 66 | 6 sides or f| 000002f0 61 63 65 73 20 0a 20 20 6f 63 74 61 2d 20 20 20 |aces . octa- | 00000300 20 20 38 20 73 69 64 65 73 20 6f 72 20 66 61 63 | 8 sides or fac| 00000310 65 73 20 20 20 20 20 20 20 20 0a 20 20 64 65 63 |es . dec| 00000320 61 2d 20 20 20 20 20 31 30 20 73 69 64 65 73 20 |a- 10 sides | 00000330 6f 72 20 66 61 63 65 73 20 20 20 20 20 20 20 72 |or faces r| 00000340 68 6f 6d 62 69 20 2d 20 61 20 34 20 73 69 64 65 |hombi - a 4 side| 00000350 64 20 70 6f 6c 79 67 6f 6e 2c 20 77 69 74 68 20 |d polygon, with | 00000360 61 6c 6c 20 0a 20 20 64 6f 64 65 63 61 2d 20 20 |all . dodeca- | 00000370 20 31 32 20 73 69 64 65 73 20 6f 72 20 66 61 63 | 12 sides or fac| 00000380 65 73 20 20 20 20 20 20 20 20 20 20 20 73 69 64 |es sid| 00000390 65 73 20 65 71 75 61 6c 20 62 75 74 20 6e 6f 74 |es equal but not| 000003a0 20 61 6c 6c 20 61 6e 67 6c 65 73 0a 20 20 69 63 | all angles. ic| 000003b0 6f 73 61 2d 20 20 20 20 32 30 20 73 69 64 65 73 |osa- 20 sides| 000003c0 20 6f 72 20 66 61 63 65 73 20 20 20 20 20 20 20 | or faces | 000003d0 0a 20 20 74 72 69 61 63 6f 6e 74 61 2d 33 30 20 |. triaconta-30 | 000003e0 73 69 64 65 73 20 6f 72 20 66 61 63 65 73 20 20 |sides or faces | 000003f0 20 20 20 20 20 64 65 6c 74 61 20 2d 20 61 20 74 | delta - a t| 00000400 72 69 61 6e 67 6c 65 2c 20 6f 72 20 33 20 73 69 |riangle, or 3 si| 00000410 64 65 64 20 70 6f 6c 79 67 6f 6e 0a 20 20 3f 3f |ded polygon. ??| 00000420 3f 20 20 20 20 20 20 20 36 30 20 73 69 64 65 73 |? 60 sides| 00000430 20 6f 72 20 66 61 63 65 73 20 20 20 20 20 20 20 | or faces | 00000440 20 20 20 77 68 69 63 68 20 6c 6f 6f 6b 73 20 6c | which looks l| 00000450 69 6b 65 20 74 68 65 20 47 72 65 65 6b 20 6c 65 |ike the Greek le| 00000460 74 74 65 72 20 44 0a 0a 41 6e 74 69 70 72 69 73 |tter D..Antipris| 00000470 6d 0a 20 20 20 61 20 70 6f 6c 79 68 65 64 72 6f |m. a polyhedro| 00000480 6e 20 6d 61 64 65 20 77 69 74 68 20 74 77 6f 20 |n made with two | 00000490 6f 70 70 6f 73 69 74 65 20 66 61 63 65 73 20 69 |opposite faces i| 000004a0 64 65 6e 74 69 63 61 6c 20 72 65 67 75 6c 61 72 |dentical regular| 000004b0 20 70 6f 6c 79 67 6f 6e 73 2c 0a 20 20 20 77 69 | polygons,. wi| 000004c0 74 68 20 6e 20 73 69 64 65 73 2c 20 61 6e 64 20 |th n sides, and | 000004d0 74 68 65 20 6f 74 68 65 72 20 66 61 63 65 73 20 |the other faces | 000004e0 6d 61 64 65 20 75 70 20 6f 66 20 32 6e 20 65 71 |made up of 2n eq| 000004f0 75 69 6c 61 74 65 72 61 6c 20 74 72 69 61 6e 67 |uilateral triang| 00000500 6c 65 73 0a 0a 44 75 61 6c 73 0a 20 32 20 70 6f |les..Duals. 2 po| 00000510 6c 79 68 65 64 72 61 20 61 72 65 20 64 75 61 6c |lyhedra are dual| 00000520 73 20 69 66 20 74 68 65 20 76 65 72 74 69 63 65 |s if the vertice| 00000530 73 20 6f 66 20 6f 6e 65 20 63 61 6e 20 62 65 20 |s of one can be | 00000540 70 75 74 20 69 6e 74 6f 20 61 20 6f 6e 65 2d 74 |put into a one-t| 00000550 6f 2d 6f 6e 65 20 0a 20 63 6f 72 72 65 73 70 6f |o-one . correspo| 00000560 6e 64 65 6e 63 65 20 77 69 74 68 20 74 68 65 20 |ndence with the | 00000570 63 65 6e 74 72 65 73 20 6f 66 20 74 68 65 20 66 |centres of the f| 00000580 61 63 65 73 20 6f 66 20 74 68 65 20 6f 74 68 65 |aces of the othe| 00000590 72 2e 0a 0a 41 72 63 68 69 6d 65 64 65 61 6e 20 |r...Archimedean | 000005a0 6f 72 20 73 65 6d 69 2d 72 65 67 75 6c 61 72 20 |or semi-regular | 000005b0 73 6f 6c 69 64 73 0a 20 31 33 20 70 6f 6c 79 68 |solids. 13 polyh| 000005c0 65 64 72 61 20 6d 61 64 65 20 66 72 6f 6d 20 6d |edra made from m| 000005d0 6f 72 65 20 74 68 61 6e 20 6f 6e 65 20 6b 69 6e |ore than one kin| 000005e0 64 20 6f 66 20 72 65 67 75 6c 61 72 20 70 6f 6c |d of regular pol| 000005f0 79 67 6f 6e 2c 0a 20 20 77 69 74 68 20 61 6c 6c |ygon,. with all| 00000600 20 76 65 72 74 69 63 65 73 20 65 71 75 61 6c 2e | vertices equal.| 00000610 0a 20 20 35 20 61 72 65 20 6d 61 64 65 20 62 79 |. 5 are made by| 00000620 20 74 72 75 6e 63 61 74 69 6e 67 20 74 68 65 20 | truncating the | 00000630 50 6c 61 74 6f 6e 69 63 20 73 6f 6c 69 64 73 0a |Platonic solids.| 00000640 20 20 32 20 61 72 65 20 27 71 75 61 73 69 2d 72 | 2 are 'quasi-r| 00000650 65 67 75 6c 61 72 27 20 77 69 74 68 20 6f 6e 6c |egular' with onl| 00000660 79 20 32 20 6b 69 6e 64 73 20 6f 66 20 66 61 63 |y 2 kinds of fac| 00000670 65 73 2c 20 65 61 63 68 20 6f 6e 65 20 65 6e 74 |es, each one ent| 00000680 69 72 65 6c 79 0a 20 20 20 20 73 75 72 72 6f 75 |irely. surrou| 00000690 6e 64 65 64 20 62 79 20 74 68 65 20 6f 74 68 65 |nded by the othe| 000006a0 72 0a 20 20 32 20 61 72 65 20 6d 61 64 65 20 62 |r. 2 are made b| 000006b0 79 20 74 72 75 6e 63 61 74 69 6e 67 20 74 68 65 |y truncating the| 000006c0 20 71 75 61 73 69 2d 72 65 67 75 6c 61 72 20 6f | quasi-regular o| 000006d0 6e 65 73 0a 20 20 32 20 72 68 6f 6d 62 69 2d 2a |nes. 2 rhombi-*| 000006e0 2a 2a 0a 20 20 31 20 73 6e 75 62 20 63 75 62 65 |**. 1 snub cube| 000006f0 0a 20 20 31 20 73 6e 75 62 20 64 6f 64 65 63 61 |. 1 snub dodeca| 00000700 68 65 64 72 6f 6e 20 0a 0a 43 6f 6d 70 6f 75 6e |hedron ..Compoun| 00000710 64 0a 20 70 6f 6c 79 68 65 64 72 6f 6e 20 6d 61 |d. polyhedron ma| 00000720 64 65 20 62 79 20 63 6f 6d 62 69 6e 69 6e 67 20 |de by combining | 00000730 32 20 6f 72 20 6d 6f 72 65 20 50 6c 61 74 6f 6e |2 or more Platon| 00000740 69 63 20 73 6f 6c 69 64 73 20 77 69 74 68 20 74 |ic solids with t| 00000750 68 65 20 73 61 6d 65 20 63 65 6e 74 72 65 0a 0a |he same centre..| 00000760 43 6f 6e 67 72 75 65 6e 74 0a 20 69 64 65 6e 74 |Congruent. ident| 00000770 69 63 61 6c 6c 79 20 65 71 75 61 6c 0a 0a 43 6f |ically equal..Co| 00000780 6e 76 65 78 20 70 6f 6c 79 67 6f 6e 0a 20 20 20 |nvex polygon. | 00000790 6f 6e 65 20 77 69 74 68 20 61 6c 6c 20 74 68 65 |one with all the| 000007a0 20 61 6e 67 6c 65 73 20 62 65 74 77 65 65 6e 20 | angles between | 000007b0 69 74 73 20 65 64 67 65 73 20 6c 65 73 73 20 74 |its edges less t| 000007c0 68 61 6e 20 31 38 30 20 64 65 67 72 65 65 73 0a |han 180 degrees.| 000007d0 0a 43 6f 6e 76 65 78 20 70 6f 6c 79 68 65 64 72 |.Convex polyhedr| 000007e0 6f 6e 0a 20 20 20 6f 6e 65 20 77 69 74 68 20 61 |on. one with a| 000007f0 6c 6c 20 69 74 73 20 64 69 68 65 64 72 61 6c 20 |ll its dihedral | 00000800 61 6e 67 6c 65 73 20 6c 65 73 73 20 74 68 61 6e |angles less than| 00000810 20 31 38 30 20 64 65 67 72 65 65 73 0a 0a 44 65 | 180 degrees..De| 00000820 6c 74 61 68 65 64 72 6f 6e 0a 20 20 68 61 73 20 |ltahedron. has | 00000830 66 61 63 65 73 20 6d 61 64 65 20 6f 6e 6c 79 20 |faces made only | 00000840 66 72 6f 6d 20 74 72 69 61 6e 67 6c 65 73 2c 20 |from triangles, | 00000850 75 73 75 61 6c 6c 79 20 65 71 75 69 6c 61 74 65 |usually equilate| 00000860 72 61 6c 0a 0a 44 69 68 65 64 72 61 6c 20 61 6e |ral..Dihedral an| 00000870 67 6c 65 0a 20 20 69 6e 74 65 72 6e 61 6c 20 61 |gle. internal a| 00000880 6e 67 6c 65 20 62 65 74 77 65 65 6e 20 32 20 66 |ngle between 2 f| 00000890 61 63 65 73 20 77 68 69 63 68 20 6d 65 65 74 20 |aces which meet | 000008a0 61 6c 6f 6e 67 20 61 20 63 6f 6d 6d 6f 6e 20 65 |along a common e| 000008b0 64 67 65 0a 0a 45 64 67 65 20 6f 66 20 61 20 70 |dge..Edge of a p| 000008c0 6f 6c 79 68 65 64 72 6f 6e 0a 20 20 6c 69 6e 65 |olyhedron. line| 000008d0 20 77 68 65 72 65 20 74 77 6f 20 66 61 63 65 73 | where two faces| 000008e0 20 6d 65 65 74 0a 0a 45 6e 74 61 6e 74 69 6f 6d | meet..Entantiom| 000008f0 6f 72 70 68 69 63 0a 20 20 61 20 70 6f 6c 79 68 |orphic. a polyh| 00000900 65 64 72 6f 6e 20 77 68 69 63 68 20 63 61 6e 20 |edron which can | 00000910 65 78 69 73 74 20 69 6e 20 74 77 6f 20 66 6f 72 |exist in two for| 00000920 6d 73 2c 20 6c 65 66 74 20 61 6e 64 20 72 69 67 |ms, left and rig| 00000930 68 74 20 68 61 6e 64 65 64 2c 0a 20 20 66 6f 72 |ht handed,. for| 00000940 20 65 78 61 6d 70 6c 65 2c 20 74 68 65 20 73 6e | example, the sn| 00000950 75 62 20 63 75 62 65 20 0a 0a 46 61 63 65 20 6f |ub cube ..Face o| 00000960 66 20 61 20 70 6f 6c 79 68 65 64 72 6f 6e 0a 20 |f a polyhedron. | 00000970 20 6f 6e 65 20 6f 66 20 74 68 65 20 70 6f 6c 79 | one of the poly| 00000980 67 6f 6e 73 20 6d 61 6b 69 6e 67 20 75 70 20 74 |gons making up t| 00000990 68 65 20 73 75 72 66 61 63 65 20 6f 66 20 74 68 |he surface of th| 000009a0 65 20 70 6f 6c 79 68 65 64 72 6f 6e 0a 0a 4a 6f |e polyhedron..Jo| 000009b0 68 6e 73 6f 6e 20 73 6f 6c 69 64 73 0a 20 20 61 |hnson solids. a| 000009c0 6c 6c 20 63 6f 6e 76 65 78 20 70 6f 6c 79 68 65 |ll convex polyhe| 000009d0 64 72 61 20 77 69 74 68 20 66 61 63 65 73 20 77 |dra with faces w| 000009e0 68 69 63 68 20 61 72 65 20 72 65 67 75 6c 61 72 |hich are regular| 000009f0 20 70 6f 6c 79 67 6f 6e 73 2c 20 65 78 63 6c 75 | polygons, exclu| 00000a00 64 69 6e 67 0a 20 20 74 68 65 20 50 6c 61 74 6f |ding. the Plato| 00000a10 6e 69 63 20 61 6e 64 20 41 72 63 68 69 6d 65 61 |nic and Archimea| 00000a20 64 65 61 6e 20 73 6f 6c 69 64 73 20 61 6e 64 20 |dean solids and | 00000a30 74 68 65 20 69 6e 66 69 6e 69 74 65 20 73 65 74 |the infinite set| 00000a40 73 20 6f 66 20 70 72 69 73 6d 73 0a 20 20 61 6e |s of prisms. an| 00000a50 64 20 61 6e 74 69 70 72 69 73 6d 73 2e 20 20 0a |d antiprisms. .| 00000a60 0a 4b 65 70 6c 65 72 2f 50 6f 69 6e 73 6f 74 20 |.Kepler/Poinsot | 00000a70 73 6f 6c 69 64 73 0a 20 20 73 69 6d 69 6c 61 72 |solids. similar| 00000a80 20 74 6f 20 50 6c 61 74 6f 6e 69 63 20 73 6f 6c | to Platonic sol| 00000a90 69 64 73 20 62 75 74 20 77 69 74 68 20 73 74 61 |ids but with sta| 00000aa0 72 20 70 6f 6c 79 67 6f 6e 73 20 61 73 20 66 61 |r polygons as fa| 00000ab0 63 65 73 2e 0a 20 20 63 6f 6d 70 6f 75 6e 64 73 |ces.. compounds| 00000ac0 20 6d 61 64 65 20 66 72 6f 6d 20 61 20 72 65 67 | made from a reg| 00000ad0 75 6c 61 72 20 70 6f 6c 79 67 6f 6e 20 61 6e 64 |ular polygon and| 00000ae0 20 69 74 73 20 64 75 61 6c 20 73 74 75 63 6b 20 | its dual stuck | 00000af0 74 6f 67 65 74 68 65 72 20 73 6f 20 74 68 61 74 |together so that| 00000b00 0a 20 20 74 68 65 69 72 20 65 64 67 65 73 20 62 |. their edges b| 00000b10 69 73 65 63 74 20 61 74 20 72 69 67 68 74 20 61 |isect at right a| 00000b20 6e 67 6c 65 73 2e 0a 0a 20 20 54 68 65 79 20 61 |ngles... They a| 00000b30 72 65 20 74 68 65 20 53 74 65 6c 6c 61 20 4f 63 |re the Stella Oc| 00000b40 74 61 6e 67 75 6c 61 2c 20 74 68 65 20 67 72 65 |tangula, the gre| 00000b50 61 74 20 69 63 6f 73 61 68 65 64 72 6f 6e 20 61 |at icosahedron a| 00000b60 6e 64 20 74 68 65 20 33 20 73 74 65 6c 6c 61 74 |nd the 3 stellat| 00000b70 69 6f 6e 73 0a 20 20 6f 66 20 74 68 65 20 64 6f |ions. of the do| 00000b80 64 65 63 61 68 65 64 72 6f 6e 0a 0a 4e 65 74 20 |decahedron..Net | 00000b90 2d 20 73 65 65 20 50 6c 61 6e 61 72 20 4e 65 74 |- see Planar Net| 00000ba0 0a 0a 50 6c 61 6e 61 72 20 4e 65 74 20 2d 20 61 |..Planar Net - a| 00000bb0 20 70 6c 61 6e 65 20 73 68 61 70 65 20 77 68 69 | plane shape whi| 00000bc0 63 68 20 63 61 6e 20 62 65 20 66 6f 6c 64 65 64 |ch can be folded| 00000bd0 20 69 6e 74 6f 20 61 20 70 6f 6c 79 68 65 64 72 | into a polyhedr| 00000be0 6f 6e 2e 20 0a 20 20 20 41 20 67 69 76 65 6e 20 |on. . A given | 00000bf0 70 6f 6c 79 68 65 64 72 6f 6e 20 6d 61 79 20 68 |polyhedron may h| 00000c00 61 76 65 20 73 65 76 65 72 61 6c 20 64 69 66 66 |ave several diff| 00000c10 65 72 65 6e 74 20 6e 65 74 73 2e 0a 20 0a 50 6c |erent nets.. .Pl| 00000c20 61 74 6f 6e 69 63 20 73 6f 6c 69 64 73 20 0a 20 |atonic solids . | 00000c30 20 20 54 68 65 20 66 69 76 65 20 6d 61 64 65 20 | The five made | 00000c40 66 72 6f 6d 20 63 6f 6e 76 65 78 20 72 65 67 75 |from convex regu| 00000c50 6c 61 72 20 70 6f 6c 79 67 6f 6e 73 20 6f 66 20 |lar polygons of | 00000c60 74 68 65 20 73 61 6d 65 20 6b 69 6e 64 2c 20 0a |the same kind, .| 00000c70 20 20 20 77 69 74 68 20 61 6c 6c 20 76 65 72 74 | with all vert| 00000c80 69 63 65 73 20 69 64 65 6e 74 69 63 61 6c 20 61 |ices identical a| 00000c90 6e 64 20 61 6c 6c 20 64 69 68 65 64 72 61 6c 20 |nd all dihedral | 00000ca0 61 6e 67 6c 65 73 20 65 71 75 61 6c 20 0a 0a 50 |angles equal ..P| 00000cb0 6f 6c 79 67 6f 6e 0a 20 20 20 61 20 70 6c 61 6e |olygon. a plan| 00000cc0 65 20 66 69 67 75 72 65 20 62 6f 75 6e 64 65 64 |e figure bounded| 00000cd0 20 62 79 20 73 74 72 61 69 67 68 74 20 65 64 67 | by straight edg| 00000ce0 65 73 20 61 6e 64 20 76 65 72 74 69 63 65 73 0a |es and vertices.| 00000cf0 0a 50 6f 6c 79 68 65 64 72 6f 6e 0a 20 20 20 61 |.Polyhedron. a| 00000d00 20 73 65 74 20 6f 66 20 70 6f 6c 79 67 6f 6e 73 | set of polygons| 00000d10 20 65 6e 63 6c 6f 73 69 6e 67 20 61 20 70 6f 72 | enclosing a por| 00000d20 74 69 6f 6e 20 6f 66 20 33 44 20 73 70 61 63 65 |tion of 3D space| 00000d30 0a 0a 50 72 69 73 6d 0a 20 20 20 61 20 70 6f 6c |..Prism. a pol| 00000d40 79 68 65 64 72 6f 6e 20 6d 61 64 65 20 77 69 74 |yhedron made wit| 00000d50 68 20 74 77 6f 20 6f 70 70 6f 73 69 74 65 20 66 |h two opposite f| 00000d60 61 63 65 73 20 69 64 65 6e 74 69 63 61 6c 20 72 |aces identical r| 00000d70 65 67 75 6c 61 72 20 70 6f 6c 79 67 6f 6e 73 2c |egular polygons,| 00000d80 20 0a 20 20 20 77 69 74 68 20 6e 20 73 69 64 65 | . with n side| 00000d90 73 20 61 6e 64 20 74 68 65 20 6f 74 68 65 72 20 |s and the other | 00000da0 66 61 63 65 73 20 20 6e 20 73 71 75 61 72 65 73 |faces n squares| 00000db0 0a 0a 50 79 72 61 6d 69 64 0a 20 20 20 61 20 70 |..Pyramid. a p| 00000dc0 6f 6c 79 68 65 64 72 6f 6e 20 77 69 74 68 20 61 |olyhedron with a| 00000dd0 20 62 61 73 65 20 61 6e 64 20 74 72 69 61 6e 67 | base and triang| 00000de0 75 6c 61 72 20 66 61 63 65 73 20 61 6c 6c 20 63 |ular faces all c| 00000df0 6f 6e 6e 65 63 74 69 6e 67 20 74 68 65 20 62 61 |onnecting the ba| 00000e00 73 65 0a 20 20 20 74 6f 20 61 20 73 69 6e 67 6c |se. to a singl| 00000e10 65 20 70 6f 69 6e 74 20 61 62 6f 76 65 20 69 74 |e point above it| 00000e20 2e 20 54 68 65 20 62 61 73 65 20 69 73 20 75 73 |. 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