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1.1 root 1: .EQ
2: delim $$
3: .EN
4: .TH POLY 5 bowell
5: .CT 1 inst_info
6: .SH NAME
7: poly \- polyhedron database
8: .SH DESCRIPTION
9: The directory
10: .B /usr/lib/polyhedra
11: contains an index file and many polyhedron description files,
12: each describing a solid polyhedron and its (not necessarily unique) planar net.
13: Each line of the index file consists of a polyhedron's number followed
14: by a horizontal tab and the polyhedron's name.
15: The polyhedron's number is also the name of its description file.
16: The routines of
17: .IR poly (3)
18: read such description files.
19: .PP
20: Each description file consists of a number of fields.
21: Each field begins with a line consisting of
22: .L :
23: and the field name.
24: The field continues until the next header line or end of file.
25: Some fields contain
26: .IR values ,
27: which consist of a floating point number
28: optionally followed by an algebraic expression enclosed in
29: .LR [] ,
30: or
31: .IR angles ,
32: which are a
33: .I value
34: in radians and optionally two more values (sin and cos) separated by
35: .LR @ .
36: The fields include,
37: but are not limited to,
38: .TF vertices
39: .TP
40: .B number
41: The polyhedron's number.
42: .PD
43: .TP
44: .B name
45: The polyhedron's name, less than 128 characters long and not capitalized.
46: .TP
47: .B symbol
48: The
49: .if n Schlaefli
50: .if t Schlaefli
51: symbol, a tab, and the Johnson symbol for the polyhedron,
52: given in
53: .IR eqn (1)
54: style with delimiters
55: .LR @@ .
56: .TP
57: .B dual
58: The name of the dual polyhedron optionally followed by a horizontal tab
59: and the number of the dual.
60: .TP
61: .B vertices
62: The first line is the number of vertices, which follow, one per line.
63: Each vertex has a coordinate (three
64: .I values
65: separated by spaces),
66: a number
67: .IR n ,
68: and
69: .I n
70: face,edge pairs that surround the vertex.
71: .TP
72: .B faces
73: The first line contains the number of faces and the maximum number of
74: vertices in any face.
75: The remaining lines are the faces, each with a vertex count
76: .IR n ,
77: followed by
78: .RI 2 n
79: vertex numbers (planar, solid),
80: .RI 2 n
81: edge numbers (planar, solid),
82: and
83: .I n
84: angles.
85: The vertices of each face are listed in the same order for both the
86: planar and solid forms:
87: counter-clockwise as viewed from above the planar net
88: (i.e. from
89: .IR z >0)
90: which generally corresponds to outside the solid polyhedron.
91: .TP
92: .B edges
93: The first line contains the number of edges.
94: Each edge is one line:
95: .IR "face1 vertex1 face2 vertex2 length angle" .
96: The length is a
97: .IR value .
98: .TP
99: .B summary
100: The three lines summarise the different kinds of faces,
101: vertices and edges respectively.
102: Each line consists of a total and a list of
103: .I "count example symbolic"
104: triples; where
105: .I example
106: is an index into the appropriate list and
107: .I symbolic
108: is given in
109: .IR eqn (1)
110: style with delimiters
111: .LR @@ .
112: .TP
113: .B EOF
114: The end of the polyhedron's description.
115: (Another polyhedron description may follow in this file.)
116: .PP
117: An expression in a
118: .I value
119: gives the exact value in the syntax of
120: .IR bc (1)
121: using these functions:
122: .if n .ig
123: $a(x) ~=~ {tan sup -1 {( x )}}$,
124: $b(x) ~=~ { ( x ) } sup { 1/3 }$,
125: $c(x) ~=~ {cos ( {x} ) }$,
126: $d(x) ~=~ {tan {( x )}}$,
127: $p ~=~ {pi}$,
128: $q(x) ~=~ {{x} sup 2}$,
129: $r(x) ~=~ {cos sup -1 {( x )}}$,
130: $s(x) ~=~ {sin ( {x} )}$,
131: $t ~=~ phi ~=~ (1 + sqrt 5 )/2$.
132: ..
133: .if t .ig
134: a(x) = arctan(x),
135: b(x) = cubrt(x),
136: c(x) = cos(x),
137: d(x) = tan(x),
138: p = pi,
139: q(x) = x^2,
140: r(x) = arccos(x),
141: s(x) = sin(x),
142: t = phi = (1 + sqrt(5))/2.
143: ..
144: The code may include assignments but does not include white space.
145: .SH FILES
146: .ta 31n
147: .F "/usr/lib/polyhedra/index "
148: index file
149: .br
150: .F "/usr/lib/polyhedra/[0-9]* "
151: description files
152: .SH "SEE ALSO"
153: .IR poly (3),
154: .IR poly (7)
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