As bordas da árvore Tikz sempre se conectam aos elementos na parte superior central

Question

\documentclass[]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,fit,shapes.geometric}
\usepackage{amssymb}

\begin{document}
\begin{tikzpicture}[]
\tikzstyle{tree_op}=[rectangle,draw=black,fill=gray!30,thick,minimum size=6mm,inner sep=0pt]
\tikzstyle{tree_subtree}=[rectangle,draw = black,densely dotted,fill=gray!30,thick,minimum size=6mm,inner sep=0pt]
\tikzstyle{triangle}=[inner sep=0pt,text=red,draw, regular polygon, regular polygon sides=3, align=center]

\tikzstyle{level 1}=[sibling distance=14mm,level distance=10mm]
\tikzstyle{level 2}=[sibling distance=14mm]
\tikzstyle{level 3}=[sibling distance=20mm]
\tikzstyle{level 4}=[sibling distance=11mm,level distance=11mm]

\node [tree_op] (root){$\rightarrow $}
  child {node [triangle] (t1) {$\triangle_1$}}
  child {node [triangle] (ti) {$\triangle_i$}}
  child {node [triangle] (tj) {$\triangle_j$}}
  child {node [triangle] (tn) {$\triangle_n$}}
;

\end{tikzpicture}
\end{document}

Tenho dois problemas com o resultado atual:

1. triângulos têm dimensões diferentes
2. as bordas devem se conectar ao vértice do triangular

Answer 1

Para resolver seus problemas, adicionei

1. um equal sizeestilo (que depende de eqparbox) que garante que os nós tenham tamanhos iguais e
2. child anchor=north.

Observe que \tikzstyleestá obsoleto, por isso o substituí pela \tikzsetsintaxe correspondente. (Eu também aumentei, level distancemas é claro que você pode desfazer isso se não gostar.)

\documentclass[]{standalone}
\usepackage{tikz}
\usepackage{eqparbox}
\newbox\nodebox
\usetikzlibrary{trees,shapes.geometric}
\usepackage{amssymb}

\begin{document}
\begin{tikzpicture}[]
\tikzset{tree_op/.style={rectangle,draw=black,fill=gray!30,thick,minimum size=6mm,inner sep=0pt},
tree_subtree/.style={rectangle,draw = black,densely dotted,fill=gray!30,thick,minimum size=6mm,inner sep=0pt},
triangle/.style={inner sep=0pt,text=red,draw, regular polygon, regular polygon
sides=3, align=center,equal size=T},
level 1/.style={sibling distance=14mm,level distance=14mm},
level 2/.style={sibling distance=14mm},
level 3/.style={sibling distance=20mm},
level 4/.style={sibling distance=11mm,level distance=11mm},
equal size/.style={execute at begin
 node={\setbox\nodebox=\hbox\bgroup},
 execute at end
 node={\egroup\eqmakebox[#1][c]{\copy\nodebox}}}}

\node [tree_op] (root){$\rightarrow $}
[child anchor=north]
  child {node [triangle] (t1) {$\triangle_1$}}
  child {node [triangle] (ti) {$\triangle_i$}}
  child {node [triangle] (tj) {$\triangle_j$}}
  child {node [triangle] (tn) {$\triangle_n$}}
;

\end{tikzpicture}
\end{document}