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 tri-oddities 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.

Links

Census

TilesCount
23
591
8100
1121
149
174
232
?1

Basic Solutions

5AC 145AD 55AE 25AF 85AH 5
5AI 115AJ 55AK 55AL 55AN 8
5AP 85AQ 85AR 55AS 85AT 11
5AU 85AV 145AW 145AX 85AY 5
5AZ 85CD 55CE 115CF 85CH 8
5CI 235CJ 85CK 85CL 85CN 8
5CP 85CQ 145CR 85CS 115CT —
5CU 85CV 115CW 85CX 175CY 8
5CZ 85DE 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 85EV 115EW 8
5EX 55EY 85EZ 85FH 55FI 8
5FJ 55FK 85FL 55FN 55FP 5
5FQ 85FR 85FS 55FT 85FU 5
5FV 85FW 55FX 85FY 55FZ 5
5HI 55HJ 55HK 85HL 55HN 5
5HP 55HQ 55HR 85HS 85HT 8
5HU 85HV 115HW 55HX 55HY 5
5HZ 85IJ 85IK 85IL 85IN 5
5IP 85IQ 115IR 55IS 55IT 23
5IU 175IV 145IW 115IX 145IY 5
5IZ 85JK 55JL 55JN 55JP 5
5JQ 55JR 85JS 55JT 85JU 8
5JV 55JW 55JX 85JY 55JZ 8
5KL 85KN 55KP 85KQ 55KR 5
5KS 85KT 55KU 85KV 85KW 8
5KX 55KY 55KZ 85LN 55LP 5
5LQ 85LR 85LS 85LT 85LU 8
5LV 85LW 85LX 115LY 55LZ 8
5NP 55NQ 85NR 85NS 85NT 8
5NU 85NV 55NW 85NX 115NY 5
5NZ 55PQ 55PR 55PS 85PT 5
5PU 55PV 85PW 55PX 85PY 5
5PZ 85QR 85QS 115QT 115QU 8
5QV 115QW 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 115UW 55UX 115UY 8
5UZ 115VW 115VX 115VY 55VZ 5
5WX 55WY 85WZ 55XY 55XZ 8
5YZ 5

Holeless Variants

5AC —5AH 85AJ 145AU 475AX 14
5AZ 115CF 145CH 115CI 535CQ 17
5CR 115CV 175CY 85CZ 115DJ 8
5DK 85EH 115EJ 115EK 115ES 23
5ET —5EU 145FH 85FI 175FJ 8
5FL 85FS 145FU 85FV 175FW 14
5HI 115HJ 85HL 85HP 85HS 11
5HV 145HW 115HZ 115IK 145IQ 14
5IS 175IT —5IU —5IW 265IX 17
5IZ 115JL 85JN 85JP 85JQ 11
5JT 205JU 145JV 115JW 175JZ 11
5KT 115KU 115KV 115KZ 85LT 11
5LW 115NT 115NV 85NZ 85QU 17
5QV 145RT 115RU 115SV 145SW 20
5SX 145SZ 115TU 505TV 175TW 11
5TX 175TZ 145UV 145UX 175VW 17
5VX 175VZ 145WZ 115XZ 115YZ 8

Last revised 2025-01-18.


Back to Polyform Oddities < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]