# Icosahedron puzzle Assume a regular icosahedron (20 sided polyhedron with triangle faces). Assume 5 colors, Pink, Green, Blue, Orange, Yellow, that are each to be used 5 times as colors to edges of the shape. Given the shape and colors, is it to make each vertex contain exactly one of each color? ## Example Diagram (unsuccessful attempt) Each number to the left is a vertex Each set to its right are its neighbor vertices P G B O Y are colors Pink, Green, Blue, Orange, Yellow Each pairing describes an edge, or a connection between vertices This manual guesswork fails because it makes vertex eleven contain two Green points. ``` P G B O Y 01 { 02 03 04 05 06 } P B O Y G 02 { 01 03 06 07 11 } G B O P Y 03 { 01 02 04 07 08 } B O Y P G 04 { 01 03 05 08 09 } O Y P B G 05 { 01 04 06 09 10 } Y O P B G 06 { 01 02 05 10 11 } Y P 07 { 02 03 08 11 12 } Y P 08 { 03 04 07 09 12 } G B 09 { 04 05 08 10 12 } G B 10 { 05 06 09 11 12 } G G 11 { 02 06 07 10 12 } 12 { 07 08 09 10 11 } ``` ## Purpose This repo tries to "brute force" solve the puzzle. It uses Elm as the implementation language. ## Example manual guesses ### After Blue B taken V_01 V_02 V_03 V_04 V_05 V_06 V_07 V_08 V_09 V_10 V_11 V_12 need ``` [ EV_01 V_01 V_02 B , EV_02 V_01 V_03 , EV_03 V_01 V_04 , EV_04 V_01 V_05 , EV_05 V_01 V_06 , EV_06 V_02 V_03 , EV_07 V_02 V_06 , EV_08 V_02 V_07 , EV_09 V_02 V_11 , EV_10 V_03 V_04 B , EV_11 V_03 V_07 , EV_12 V_03 V_08 , EV_13 V_04 V_05 , EV_14 V_04 V_08 , EV_15 V_04 V_09 , EV_16 V_05 V_06 B , EV_17 V_05 V_09 , EV_18 V_05 V_10 , EV_19 V_06 V_10 , EV_20 V_06 V_11 , EV_21 V_07 V_08 B , EV_22 V_07 V_11 , EV_23 V_07 V_12 , EV_24 V_08 V_09 , EV_25 V_08 V_12 , EV_26 V_09 V_10 B , EV_27 V_09 V_12 , EV_28 V_10 V_11 , EV_29 V_10 V_12 , EV_30 V_11 V_12 B ] ``` ### After Blue, Yellow Y taken V_01 V_03 V_02 V_06 V_04 V_05 V_10 V_12 V_08 V_09 V_07 V_11 need ``` [ EV_01 V_01 V_02 B , EV_02 V_01 V_03 Y , EV_03 V_01 V_04 , EV_04 V_01 V_05 , EV_05 V_01 V_06 , EV_06 V_02 V_03 , EV_07 V_02 V_06 Y , EV_08 V_02 V_07 , EV_09 V_02 V_11 , EV_10 V_03 V_04 B , EV_11 V_03 V_07 , EV_12 V_03 V_08 , EV_13 V_04 V_05 Y , EV_14 V_04 V_08 , EV_15 V_04 V_09 , EV_16 V_05 V_06 B , EV_17 V_05 V_09 , EV_18 V_05 V_10 , EV_19 V_06 V_10 , EV_20 V_06 V_11 , EV_21 V_07 V_08 B , EV_22 V_07 V_11 Y , EV_23 V_07 V_12 , EV_24 V_08 V_09 Y , EV_25 V_08 V_12 , EV_26 V_09 V_10 B , EV_27 V_09 V_12 , EV_28 V_10 V_11 , EV_29 V_10 V_12 Y , EV_30 V_11 V_12 B ] ``` ### After Blue, Yellow O taken V_01 V_02 V_03 V_04 V_05 V_09 need V_10 V_11 V_06 V_07 V_08 V_12 cant 06 10 ``` [ EV_01 V_01 V_02 B , EV_02 V_01 V_03 Y , EV_03 V_01 V_04 O , EV_04 V_01 V_05 , EV_05 V_01 V_06 , EV_06 V_02 V_03 O , EV_07 V_02 V_06 Y , EV_08 V_02 V_07 , EV_09 V_02 V_11 , EV_10 V_03 V_04 B , EV_11 V_03 V_07 , EV_12 V_03 V_08 , EV_13 V_04 V_05 Y , EV_14 V_04 V_08 , EV_15 V_04 V_09 , EV_16 V_05 V_06 B , EV_17 V_05 V_09 O , EV_18 V_05 V_10 , EV_19 V_06 V_10 , EV_20 V_06 V_11 , EV_21 V_07 V_08 B , EV_22 V_07 V_11 Y , EV_23 V_07 V_12 , EV_24 V_08 V_09 Y , EV_25 V_08 V_12 , EV_26 V_09 V_10 B , EV_27 V_09 V_12 , EV_28 V_10 V_11 , EV_29 V_10 V_12 Y , EV_30 V_11 V_12 B ] ```