Pentahex Pair Tri-Oddities

A polyhex tri-oddity is a figure with ternary symmetry formed by some number of copies of a polyhex that is not a multiple of three. Torsten Sillke first studied them in 1996.

Here I show minimal known tri-oddities for pairs of pentahexes. Please write if you find a smaller solution or solve an unsolved case.

For tri-oddities for single pentahexes, see Polyhex Tri-Oddities. For standard oddities for pentahex pairs, see Pentahex Pair Oddities.

Basic Solutions

5AC 145AD 55AE 25AF 85AH 5
5AI 115AJ 55AK 55AL 55AN 8
5AP 85AQ 85AR 55AS 85AT 11
5AU 85AV 145AW 145AX 115AY 5
5AZ 85CD 55CE 115CF 85CH 8
5CI 235CJ 85CK 85CL 85CN 8
5CP 85CQ 145CR 85CS 115CT —
5CU 85CV 115CW 85CX 175CY 11
5CZ 115DE 55DF 85DH 85DI 5
5DJ 55DK 55DL 55DN 55DP 5
5DQ 85DR 55DS 55DT 85DU 8
5DV 55DW 55DX 55DY 25DZ 8
5EF 85EH 85EI 55EJ 55EK 8
5EL 85EN 85EP 55EQ 145ER 5
5ES 175ET 175EU 115EV 115EW 11
5EX 55EY 85EZ 115FH 55FI 8
5FJ 55FK 85FL 55FN 55FP 5
5FQ 85FR 85FS 55FT 85FU 5
5FV 85FW 55FX 85FY 55FZ 5
5HI 55HJ 55HK 115HL 55HN 5
5HP 55HQ 55HR 115HS 85HT 8
5HU 85HV 175HW 55HX 55HY 5
5HZ 85IJ 85IK 85IL 85IN 5
5IP 85IQ 115IR 55IS 55IT 23
5IU 175IV 145IW 115IX 145IY 5
5IZ 115JK 55JL 55JN 55JP 5
5JQ 55JR 85JS 55JT 115JU 8
5JV 55JW 55JX 85JY 55JZ 11
5KL 85KN 55KP 85KQ 55KR 5
5KS 85KT 55KU 85KV 85KW 8
5KX 55KY 55KZ 115LN 55LP 5
5LQ 85LR 115LS 85LT 115LU 8
5LV 85LW 85LX 115LY 55LZ 8
5NP 55NQ 85NR 115NS 85NT 8
5NU 85NV 85NW 85NX 115NY 5
5NZ 55PQ 55PR 55PS 85PT 5
5PU 55PV 85PW 55PX 85PY 5
5PZ 85QR 85QS 145QT 145QU 8
5QV 145QW 25QX 55QY 85QZ 8
5RS 85RT 85RU 85RV 85RW 8
5RX 55RY 55RZ 55ST 85SU 5
5SV 115SW 145SX 85SY 55SZ 5
5TU 85TV 115TW 55TX 145TY 8
5TZ 85UV 145UW 55UX 115UY 8
5UZ 115VW 115VX 115VY 55VZ 5
5WX 55WY 85WZ 55XY 55XZ 8
5YZ 5

Holeless Variants

5AC —5AF 115AH 115AJ 175AN 11
5AU —5AV 175AW 175AX 145AZ 17
5CF 175CH 115CI —5CK 115CQ 23
5CR 115CV 175CZ 145DJ 85DK 8
5EH 145EJ 175EK 145ES 235ET —
5EU 145EV 175FH 115FI 175FJ 11
5FL 115FS 175FU 175FV 175FW 17
5HI 175HJ 85HL 115HP 85HS 14
5HT 115HU 115HW 115HZ 145IK 17
5IQ 175IS 175IT —5IU —5IW 26
5IX 175JL 85JN 85JP 85JQ 14
5JT 235JU 235JV 145JW 175KT 11
5KU 115KV 145LW 115NT 115NX 14
5NZ 145QS 175QU 175QV 175RT 11
5RU 115SV 175SW 235SX 175SZ 14
5TU —5TV 175TW 235TX 175TZ 17
5UX 175VW 175VX 175VZ 145WZ 14
5XZ 115YZ 8

Last revised 2024-06-28.


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Col. George Sicherman [ HOME | MAIL ]