.EQ delim $$ .EN .TH POLY 5 bowell .CT 1 inst_info .SH NAME poly \- polyhedron database .SH DESCRIPTION The directory .B /usr/lib/polyhedra contains an index file and many polyhedron description files, each describing a solid polyhedron and its (not necessarily unique) planar net. Each line of the index file consists of a polyhedron's number followed by a horizontal tab and the polyhedron's name. The polyhedron's number is also the name of its description file. The routines of .IR poly (3) read such description files. .PP Each description file consists of a number of fields. Each field begins with a line consisting of .L : and the field name. The field continues until the next header line or end of file. Some fields contain .IR values , which consist of a floating point number optionally followed by an algebraic expression enclosed in .LR [] , or .IR angles , which are a .I value in radians and optionally two more values (sin and cos) separated by .LR @ . The fields include, but are not limited to, .TF vertices .TP .B number The polyhedron's number. .PD .TP .B name The polyhedron's name, less than 128 characters long and not capitalized. .TP .B symbol The .if n Schlaefli .if t Schlaefli symbol, a tab, and the Johnson symbol for the polyhedron, given in .IR eqn (1) style with delimiters .LR @@ . .TP .B dual The name of the dual polyhedron optionally followed by a horizontal tab and the number of the dual. .TP .B vertices The first line is the number of vertices, which follow, one per line. Each vertex has a coordinate (three .I values separated by spaces), a number .IR n , and .I n face,edge pairs that surround the vertex. .TP .B faces The first line contains the number of faces and the maximum number of vertices in any face. The remaining lines are the faces, each with a vertex count .IR n , followed by .RI 2 n vertex numbers (planar, solid), .RI 2 n edge numbers (planar, solid), and .I n angles. The vertices of each face are listed in the same order for both the planar and solid forms: counter-clockwise as viewed from above the planar net (i.e. from .IR z >0) which generally corresponds to outside the solid polyhedron. .TP .B edges The first line contains the number of edges. Each edge is one line: .IR "face1 vertex1 face2 vertex2 length angle" . The length is a .IR value . .TP .B summary The three lines summarise the different kinds of faces, vertices and edges respectively. Each line consists of a total and a list of .I "count example symbolic" triples; where .I example is an index into the appropriate list and .I symbolic is given in .IR eqn (1) style with delimiters .LR @@ . .TP .B EOF The end of the polyhedron's description. (Another polyhedron description may follow in this file.) .PP An expression in a .I value gives the exact value in the syntax of .IR bc (1) using these functions: .if n .ig $a(x) ~=~ {tan sup -1 {( x )}}$, $b(x) ~=~ { ( x ) } sup { 1/3 }$, $c(x) ~=~ {cos ( {x} ) }$, $d(x) ~=~ {tan {( x )}}$, $p ~=~ {pi}$, $q(x) ~=~ {{x} sup 2}$, $r(x) ~=~ {cos sup -1 {( x )}}$, $s(x) ~=~ {sin ( {x} )}$, $t ~=~ phi ~=~ (1 + sqrt 5 )/2$. .. .if t .ig a(x) = arctan(x), b(x) = cubrt(x), c(x) = cos(x), d(x) = tan(x), p = pi, q(x) = x^2, r(x) = arccos(x), s(x) = sin(x), t = phi = (1 + sqrt(5))/2. .. The code may include assignments but does not include white space. .SH FILES .ta 31n .F "/usr/lib/polyhedra/index " index file .br .F "/usr/lib/polyhedra/[0-9]* " description files .SH "SEE ALSO" .IR poly (3), .IR poly (7)