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class QGraphicsHexagonItem : public QGraphicsPolygonItem
{
private:
protected:
    void mousePressEvent(QMouseEvent* MouseEvent);
public:
	QGraphicsHexagonItem(QPoint center, int radius);
};

#ifndef __QGRAPHICSHEXAGONITEM_H__
#define __QGRAPHICSHEXAGONITEM_H__

#include <QObject>
#include <QGraphicsPolygonItem>
#include <QPen>
#include <QMouseEvent>

class QGraphicsHexagonItem : public QGraphicsPolygonItem
{
private:
protected:
	void mousePressEvent(QMouseEvent* MouseEvent);
public:
	QGraphicsHexagonItem(QPoint center, int radius);
};

#endif

#include "QGraphicsHexagonItem.h"

QGraphicsHexagonItem::QGraphicsHexagonItem(QPoint center, int radius)
{
	QVector<QPoint> vector;
	int R = radius;
	int r = R*sqrt(3.0)/2;

	QPen pen;
	pen.setWidthF(2.5);
	
	vector.push_back(QPoint(center.x(), center.y()-R));
	vector.push_back(QPoint(center.x()+r, center.y()-r/2));
	vector.push_back(QPoint(center.x()+r, center.y()+r/2));
	vector.push_back(QPoint(center.x(), center.y()+R));
	vector.push_back(QPoint(center.x()-r, center.y()+r/2));
	vector.push_back(QPoint(center.x()-r, center.y()-r/2));

	this->setPolygon(QPolygon(vector));
	this->setPen(pen);
	this->setBrush(QBrush(Qt::green));
}

void QGraphicsHexagonItem::mousePressEvent(QMouseEvent* MouseEvent)
{
	//...
}

QGraphicsScene* scene = new QGraphicsScene(this);
	int width = 580;
	int height = 310;
	int space = 5;
	scene->setSceneRect(0, 0, width-2, height-2);
	int R = 15;
	int r = R*sqrt(3.0)/2;
	QPoint center(space+r, space+R);

	QPen pen;
	pen.setWidthF(2.5);

	bool t = false;
	for(int x, y=0;center.y()+R<=height-2-space;center.setY(center.y()+R+r/2),t=!t,++y)
	{
		x=0;
		for(center.setX(space+r+(t?r:0));center.x()+r<=width-2-space;center.setX(center.x()+r+r),++x)
			scene->addItem(new QGraphicsHexagonItem(center, R));
	}

	QGraphicsView* view = new QGraphicsView(scene, this);
	view->setGeometry(10, 50, width, height);
	view->show();