Go: package main

import (
	"bufio"
	"os"
	"strconv"
	"strings"
		"reflect"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

func main() {
	// 上面の色を固定してから、左右方向に回転して一致するものがあるかを調べる
	round := [][]int{
		{1,2,3,4,5,6}, {1,3,5,2,4,6}, {1,4,2,5,3,6}, {1,5,4,3,2,6}, // c1を上面に固定して回転
		{2,6,3,4,1,5}, {2,3,1,6,4,5}, {2,1,4,3,6,5}, {2,4,6,1,3,5}, // c2を上面に固定して回転
		{3,1,2,5,6,4}, {3,2,6,1,5,4}, {3,5,1,6,2,4}, {3,6,5,2,1,4}, // c3を上面に固定して回転
		{4,1,5,2,6,3}, {4,2,1,6,5,3}, {4,5,6,1,2,3}, {4,6,2,5,1,3}, // c4を上面に固定して回転
		{5,1,3,4,6,2}, {5,3,6,1,4,2}, {5,4,1,6,3,2}, {5,6,4,3,1,2}, // c5を上面に固定して回転
		{6,2,4,3,5,1}, {6,3,2,5,4,1}, {6,5,3,4,2,1}, {6,4,5,2,3,1}, // c6を上面に固定して回転

	}
	for scanner.Scan() {
		n, _ := strconv.Atoi(scanner.Text())
		if n == 0 {
			break
		}
		cubes := make([][]string, n)
		for i := 0; i < n; i++ {
			scanner.Scan()
			cubes[i] = strings.Split(scanner.Text(), " ")
		}
		check := func(a, b int) bool {
			tmp := make([]string, 6)
			for i := 0; i < 24; i++ {
				for j := 0; j < 6; j++ {
					tmp[j] = cubes[b][round[i][j]-1]
				}
				if reflect.DeepEqual(tmp, cubes[a]) {
					return true
				}
			}
			return false
		}
		tbl := make([]int, n)
		// 全ての組み合わせを調べる
		for i := 0; i < n; i++ {
			if tbl[i] == 1 {
				continue
			}
			for j := i+1; j < n; j++ {
				if check(i, j) {
					tbl[j] = 1
				}
			}
		}
		fmt.Println(sum(tbl))
	}
}

func sum(a []int) int {
	ret := 0
	for _, v := range a {
		ret += v
	}
	return ret
}

C++: #include <iostream>
#include <string>
#include <string.h>
using namespace std;

class Dice
{
public:
	Dice( char c[ 6 ] )
	{
		for( int i = 0; i < 6; ++i ){
			face[ i ] = c[ i ];
		}
		face[ 6 ] = '\0';
	}
	void rotateVertical()
	{
		char t = face[ 0 ];
		face[ 0 ] = face[ 1 ];
		face[ 1 ] = face[ 5 ];
		face[ 5 ] = face[ 4 ];
		face[ 4 ] = t;
	}
	void rotateHorizontal()
	{
		char t = face[ 1 ];
		face[ 1 ] = face[ 2 ];
		face[ 2 ] = face[ 4 ];
		face[ 4 ] = face[ 3 ];
		face[ 3 ] = t;
	}
	char roundFace( int index )
	{
		static int a[] = { 1, 2, 4, 3 };
		return face[ a[ index ] ];
	}
	int getId()
	{
		static string pattern[] = {
			"RBMGCY", "RBMCGY", "RBGMCY", "RBGCMY", "RBCMGY", "RBCGMY",
			"RYMGCB", "RYMCGB", "RYGMCB", "RYGCMB", "RYCMGB", "RYCGMB",
			"RYBGCM", "RYBCGM", "RYGBCM", "RYGCBM", "RYCBGM", "RYCGBM",
			"RYBMCG", "RYBCMG", "RYMBCG", "RYMCBG", "RYCBMG", "RYCMBG",
			"RYBMGC", "RYBGMC", "RYMBGC", "RYMGBC", "RYGBMC", "RYGMBC",
		};
		if( face[ 2 ] == 'R' || face[ 3 ] == 'R' ){
			rotateHorizontal();
		}
		while( face[ 0 ] != 'R' ){
			rotateVertical();
		}
		if( face[ 5 ] == 'Y' ){
			while( face[ 1 ] != 'B' ){
				rotateHorizontal();
			}
		}else{
			while( face[ 1 ] != 'Y' ){
				rotateHorizontal();
			}
		}
		string diceStr( face );
		for( int i = 0; i < 30; ++i ){
			if( pattern[ i ] == diceStr ){
				return i;
			}
		}
		return -1;
	}

	char face[ 6 + 1 ];
};

int main()
{
	int n;
	while( cin >> n && n ){
		int id[ 30 ];
		memset( id, 0, sizeof(id) );

		for( int i = 0; i < n; ++i ){
			string s;
			char c[ 6 ];
			for( int i = 0; i < 6; ++i ){
				cin >> s;
				c[ i ] = s[ 0 ];
			}
			Dice dice( c );
			++id[ dice.getId() ];
		}

		int ans = 0;
		for( int i = 0; i < 30; ++i ){
			if( id[ i ] > 1 ){
				ans += ( id[ i ] - 1 );
			}
		}
		cout << ans << endl;
	}

	return 0;
}

C++: #include <iostream>
#include <string>
#include <vector>
#include <map>
#include <set>
using namespace std;

short h(vector<int> &id){
	short r=0,i=0;
	for(;i<6;i++)r=r*6+id[i];
	return r;
}

// http://www.prefield.com/algorithm/misc/dice.html
enum FACE { TOP, LEFT, FRONT, BACK, RIGHT, BOTTOM };
class dice {
public:
  dice(vector<int>&v):id(v) {}
  void roll_x() { roll(TOP, BACK, BOTTOM, FRONT); }
  void roll_x2() { roll(TOP, FRONT, BOTTOM, BACK); }
  void roll_y() { roll(TOP, LEFT, BOTTOM, RIGHT); }
  void roll_y2() { roll(TOP, RIGHT, BOTTOM, LEFT); }
  void roll_z() { roll(FRONT, RIGHT, BACK, LEFT); }
  void roll_z2() { roll(FRONT, LEFT, BACK, RIGHT); }
  void all_rolls(set<short>&s){
    for (int k = 0; k < 6; (k&1?roll_y():roll_x()),++k)
      for (int i = 0; i < 4; roll_z(), ++i)
        s.insert(h(id));
  }
  vector<int> id;
private:
  void roll(FACE a, FACE b, FACE c, FACE d) {
    int tmp = id[a];
    id[a] = id[b]; id[b] = id[c];
    id[c] = id[d]; id[d] = tmp;
  }
};

int main(){
	map<char,int>m;
	m['R']=0,m['Y']=1,m['B']=2,m['M']=3,m['G']=4,m['C']=5;
	string str;
	vector<int>v(6);
	int n,i,j,r;
	for(;cin>>n,n;){
		set<short>s;
		for(r=i=0;i<n;i++){
			for(j=0;j<6;j++)cin>>str,v[j]=m[str[0]];
			if(s.find(h(v))!=s.end())r++;
			else{
				dice d(v);
				d.all_rolls(s);
			}
		}
		cout<<r<<endl;
	}
}

C++: 
// Trouble in Shinagawa's Artifacts
//  URL: http://rose.u-aizu.ac.jp/onlinejudge/ProblemSet/description.jsp?id=0198&lang=jp

#include <cstdio>
#include <cstring>
#include <vector>
#include <set>

// Ö
std::vector <int> rotate_h( std::vector <int> box );
std::vector <int> rotate_v( std::vector <int> box );

// ¡Éñ]³¹éÖ
std::vector <int> rotate_h( std::vector <int> box )
{
	// ¡ñ]
	// c1, c2, c3, c4, c5, c6 : default
	// c3, c2, c6, c1, c5, c4
	
	int tmp	= box[0];
	box[0]	= box[2];
	box[2]	= box[5];
	box[5]	= box[3];
	box[3]	= tmp;

	return box;

}

// cÉñ]³¹éÖ
std::vector <int> rotate_v( std::vector <int> box )
{
	// cñ]
	// c1, c2, c3, c4, c5, c6 : default
	// c5, c1, c3, c4, c6, c2

	int tmp = box[0];
	box[0] = box[4];
	box[4] = box[5];
	box[5] = box[1];
	box[1] = tmp;

	return box;

}

// Gg[|Cg
int main()
{

	// Ï
	int n;
	int answer;
	char color[32];
	std::vector <int> box( 6, 0 );
	std::set < std::vector <int> > table;

	while( 1 )
	{
		// ú»
		answer = 0;
		table.clear();
		for( int i = 0; i < 6; ++i )
		{
			box[i] = 0;
		}

		// üÍ
		std::fflush( stdin );
		std::scanf( "%d", &n );

		// üÍÌIíèF[ÐÆÂ
		if( n == 0 ) break;

		// nÌ¾¯ÇÝÞ
		for( int i = 0; i < n; ++i )
		{
			std::fflush( stdin );

			// FîñðüÍ
			for( int j = 0; j < 6; ++j )
			{
				std::scanf( "%s", color );

				// µ¢â·¢æ¤É¶ñ¨®ÉÏ·
				// F: Red, Yellow, Blue, Magenta, Green, Cyan
				if( std::strcmp( "Red", color ) == 0 )
					box[j] = 1;
				else if( std::strcmp( "Yellow", color ) == 0 )
					box[j] = 2;
				else if( std::strcmp( "Blue", color ) == 0 )
					box[j] = 3;
				else if( std::strcmp( "Magenta", color ) == 0 )
					box[j] = 4;
				else if( std::strcmp( "Green", color ) == 0 )
					box[j] = 5;
				else if( std::strcmp( "Cyan", color ) == 0 )
					box[j] = 6;
			}

			// insertÌOÉ¯¶àÌªÈ¢©T·
			// ¯¶àÌª Á½çJEg
			if( table.find( box ) != table.end() )
			{
				++answer;
			}

			// insertµÄ¨­
			// ¡¨cx3ð4ñ
			for( int j = 0; j < 4; ++j )
			{
				if( j > 0 )
				{
					box = rotate_h( box );
				}
				table.insert( box );
				
				// c
				for( int k = 0; k < 4; ++k )
				{
					box = rotate_v( box );
					table.insert( box );
				}
			}

		}

		// oÍ
		std::printf( "%d\n", answer );

	}

} // main()