unicode-math + TeX Gyre Termes Math without \bigstar?

Question

When I use TeX Gyre Termes Math with unicode-math like in the example I can't get the \bigstar symbol. It seems that the font does not have a bigstar at U-2605. Is there a way to re-define the \bigstar command to deliver a scaled version of the \star command to fit the math sizes? BTW, \ast is a lot bigger than \star; I wouldn't have to bother about \bigstar if \star were of the same size as \ast.

\documentclass{minimal}
\usepackage{fontspec}
\setmainfont[Numbers=OldStyle, Ligatures=TeX]{TeX Gyre Termes}
\usepackage[math-style=ISO]{unicode-math}%
\setmathfont[Numbers=Lining]{TeX Gyre Termes Math}
\begin{document}
\begin{equation}
    (\mathbb{Z}(p))^\star \star \qquad 
    \left(\mathbb{Z}(p)\right)^{\bigstar} \bigstar\qquad
    (\mathbb{Z}(p))^\ast \ast
\end{equation}
    ---$\symbol{"2605}$\symbol{"2605}---
\end{document}

Answer 1

The glyph corresponding to U+2605 is not available in TeX Gyre Termes (text and math). You can use the glyph from another font:

\documentclass{article}

\usepackage[math-style=ISO]{unicode-math}

\setmainfont[Numbers=OldStyle, Ligatures=TeX]{TeX Gyre Termes}

\setmathfont[Numbers=Lining]{TeX Gyre Termes Math}
\setmathfont[range=\bigstar]{XITS Math}
\setmathfont[range=\int]{TeX Gyre Termes Math} % just to get parameters from this font

\begin{document}

\begin{equation}
(\mathbb{Z}(p))^\star \star \qquad
\mathbb{Z}(p))^{\bigstar} \bigstar\qquad
(\mathbb{Z}(p))^\ast \ast
\end{equation}

\end{document}

Note that Numbers=Lining for TeX Gyre Termes Math is meaningless. Also, using oldstyle figures with Times New Roman (or any lookalike thereof) is an anachronism.

Note also that \bigstar is classified as a math ordinary symbol, so you need \mathbin{\bigstar} when you want it to act as a binary operation symbol.

Answer 2

You may enlarge the original star with help of the relsize package. The height is not absolutely identical like this, but the approach is quite easy and you are using the same font for both symbols.

% arara: lualatex

\documentclass{article}
\usepackage{fontspec}
\setmainfont[Numbers=OldStyle, Ligatures=TeX]{texgyretermes-regular.otf}
\usepackage[math-style=ISO]{unicode-math}%
\setmathfont{texgyretermes-math.otf}
\usepackage{relsize}
\newcommand{\STAR}{\mathlarger{\mathlarger{\star}}}

\begin{document}        
$\STAR\star\ast$

\newdimen\astheight
\setbox0=\hbox{$\ast$}
\astheight=\ht0 \advance\astheight by \dp0
The height of the $\ast$ symbol is: \the\astheight

\newdimen\STARheight
\setbox0=\hbox{$\STAR$}
\STARheight=\ht0 \advance\STARheight by \dp0
The height of the $\STAR$ symbol is: \the\STARheight

$
(\mathbb{Z}(p))^\star \star \qquad
\mathbb{Z}(p))^{\STAR} \STAR \qquad
(\mathbb{Z}(p))^\ast \ast
$
\end{document}