product_2_8_di_1:  S^1xS^1
product_3_10_di_1:  S^2xS^1
product_4_12_di_1:  S^2xS^2
product_4_12_di_2:  S^3xS^1
product_4_12_cy_1:  S^2xS^2
product_4_12_cy_2:  S^2xS^2
product_5_14_di_1:  S^4xS^1
product_5_14_di_2:  S^3xS^2
product_6_16_di_1:  S^3xS^3
product_6_16_di_2:  S^5xS^1
product_6_16_cy_1:  S^3xS^3
product_7_18_di_1:  S^6xS^1
product_7_18_di_2:  S^5xS^2
product_7_18_di_3:  S^4xS^3
product_8_20_di_1:  S^4xS^4
product_8_20_di_2:  S^7xS^1
product_8_20_di_3:  S^5xS^3