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 <bits/stdc++.h>
using namespace std ;

#define pb(n) push_back(n)
#define fi first
#define se second
#define all(r) (r).begin(),(r).end()
#define vmax(ary) *max_element(all(ary))
#define vmin(ary) *min_element(all(ary))
#define debug(x) cout<<#x<<": "<<x<<endl
#define fcout(n) cout<<fixed<<setprecision((n))
#define scout(n) cout<<setw(n)
#define vary(type,name,size,init) vector< type> name(size,init)
#define vvl(v,w,h,init) vector<vector<ll>> v(w,vector<ll>(h,init))
#define mp(a,b) make_pair(a,b)

#define rep(i,n) for(int i = 0; i < (int)(n);++i)
#define REP(i,a,b) for(int i = (a);i < (int)(b);++i)
#define repi(it,array) for(auto it = array.begin(),end = array.end(); it != end;++it)
#define repa(n,array) for(auto &n :(array))

using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using dict = map<string,int>;
using pii = pair<int,int> ;
using pll = pair<ll,ll> ;

const int mod = 1000000007;
constexpr int inf = ((1<<30)-1)*2+1 ;
constexpr double PI = acos(-1.0) ;
double eps = 1e-10 ;
const int dy[] = {-1,0,1,0,1,-1,1,-1};
const int dx[] = {0,-1,0,1,1,-1,-1,1};

inline bool value(int x,int y,int w,int h){
  return (x >= 0 && x < w && y >= 0 && y < h);
}

template<typename T>
void Unique(vector<T> &v){
  sort(all(v));
  v.erase(unique(all(v)),v.end());
}
template<typename T,typename U>
ll FindErase(T &v,U tar){
  ll cnt = 0;
  for(auto it = v.begin(); it != v.end();){
    if(*it == tar){
      it = v.erase(it);
      ++cnt;
    }
    else{
      ++it;
    }
  }
  return cnt;
}

enum{
  t = 0,f ,r ,b ,l ,d ,
};
class Dice{
  public:
    array<int,6> D;
    Dice(){
      D = {1,2,3,4,5,6};
    }
    Dice(array<int,6> d){
      D = d;
    }
    void Spin(int dir){
      if(dir == l){//
        swap(D[t],D[r]);
        swap(D[r],D[d]);
        swap(D[d],D[l]);
      }
      else if(dir == r){
        swap(D[t],D[l]);
        swap(D[l],D[d]);
        swap(D[d],D[r]);
      }
      else if(dir == f){
        swap(D[t],D[b]);
        swap(D[b],D[d]);
        swap(D[d],D[f]);
      }
      else if(dir == b){
        swap(D[t],D[f]);
        swap(D[f],D[d]);
        swap(D[d],D[b]);
      }
      else if(dir == d){//leftspin
        swap(D[f],D[r]);
        swap(D[r],D[b]);
        swap(D[b],D[l]);
      }
      else if(dir == t){
        swap(D[f],D[l]);
        swap(D[l],D[b]);
        swap(D[b],D[r]);
      }
    }
    void MatchDice(int T,int F){
      rep(i,4){
        Spin(r);
        if(D[t] == T)break;
      }
      if(D[t] != T){
        rep(i,4){
          Spin(f);
          if(D[t] == T)break;
        }
      }
      rep(i,4){
        Spin(t);
        if(D[f] == F) break;
      }
    }
    int& operator[](const int i){
      return D[i];
    }
    bool operator==(Dice& di2){
      rep(i,4){
        di2.Spin(r);
        rep(j,4){
          di2.Spin(t);
          rep(k,4){
            di2.Spin(r);
            if(D == di2.D){
              return true;
            }
          }
        }
      }
      return false;
    }
    friend ostream& operator<<(ostream& os,const Dice& di){
      os << "t f r l b d\n" ;
      rep(i,6){
        if(i) os << ' ';
        os << di.D[i] ;
      }
      return os;
    }
};

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  map<string,int> m;
  m["Cyan"] = 0,m["Yellow"] =1,m["Red"]=2,m["Magenta"] = 3, m["Green"] = 4, m["Blue"] = 5;
  ll n;
  while(cin >> n && n){
    vector<Dice> di(n);
    string s;
    vector<Dice> st;
    rep(i,n){
      rep(j,6){
        cin >> s;
        di[i][j] = m[s];
      }
      if(st.size() == 0){
        st.push_back(di[i]);
      }
      rep(j,st.size()){
        if(st[j] == di[i]){
          break;
        }
        if(j == st.size()-1){
          st.push_back(di[i]);
        }
      }
    }
    cout << n - st.size()<<endl;
  }
  return 0;
}

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>

#define FOREACH( TYPE, TARGET, IT ) \
	for( (TYPE)::iterator IT = (TARGET).begin(); IT != (TARGET).end(); ++(IT) )

// 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()
{
	// §ûÌÌ6ÊðyLÅFt¯µ½àÌðìiÆµÄoWµ½
	// §ûÌðñ]³¹éÆ¯¶gÝí¹ÉÈÁÄµÜ¤±ÆÉCªt¢½
	// d¡ð³­µ½Æ«ÇÁÅ½Âìè¼·Kvª é©ßé



	// 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;
				continue;
			}

			// 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 );
				}
			}
		}

		// debug
		std::printf( "%d\n", answer );

	}

} // main()