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I know that \fontdimen<num> returns some dimensions associated with the current font. What are they?

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They are clearly explained in the TeXbook. –  Martin Schröder Jan 2 '13 at 22:17
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@MartinSchröder If the answer being in the TeX (or LaTeX) Book was grounds for not answering a question, this site would have a lot less traffic. –  David Carlisle Jan 3 '13 at 0:16

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up vote 28 down vote accepted

For text fonts there are 7 parameters

1 slant per pt (used for italic correction)

2 interword space (standard width of the space )

3 interword stretch (amount the space can stretch)

4 interword shrink (amount the space can shrink)

5 x-height (the value for the ex unit)

6 quad-width (The em unit)

7 extra space (controls additional space after sentence punctuation)


Math symbol fonts (\fam=2) must have at least 22 parameters, and extension fonts (used for large brackets etc) must have at least 13 parameters.

These font parameters are as followed (prefixed with s if they are used from \fam2 and prefixed with x if used from extension fonts (normally \fam3)

The exact use of each parameter is described in appendix G of the TeXBook a brief (but hopefully correct) indication of the use of each parameter is given below.

s5 x-height (ex unit length)

s6 quad (em unit length)

s8 num1 (shift standard size numerator up by this amount)

s9 num2 (alternative numerator shift)

s10 num3 (alternative numerator shift)

s11 denom1 (shift standard size denominator down by this amount)

s12 denom2 (alternative denominator shift)

s13 sup1 (alternative superscript position)

s14 sup2 (alternative superscript position)

s15 sup3 (alternative superscript position)

s16 sub1 (alternative subscript position)

s17 sub2 (alternative subscript position)

s18 sup-drop (further control of superscript positioning)

s19 sub-drop (further control of subscript positioning)

s20 delim1 (minimum display delimiter size)

s21 delim2 (minimum text delimiter size)

s22 axis-height (The height of the axis on which large operators and delimiters are centred)

x8 default-rule-thickness (default fraction line, also minimum separation between sub and super scripts)

x9 big-op-spacing1 (controls limits spacing)

x10 big-op-spacing2 (controls limits spacing)

x11 big-op-spacing3 (controls limits spacing)

x12 big-op-spacing4 (controls limits spacing)

x13 big-op-spacing5 (controls limits spacing)

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Is this heptaphoby? –  mafp Jan 2 '13 at 22:10
    
@mafp :-) The first 7 text-oriented parameters are the same in text and math fonts but don't really play a part in math setting except for s5 and s6 –  David Carlisle Jan 2 '13 at 23:27

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