There are 32 square rectates, divided up into 3 regiments of 8, 1 regiment of 5, and 1 regiment of 3. One of the 32 is a repeat, meaning there are 31 new honeycombs. The regiments are based off of riddoh, rishexah, rocth, squah, and risdoe. The first of each regiment is orientable, and so are hahat, ciddih hathahs, chath, ohazh, rohah, siddohohaha, shaho, sahas, hassas, and rishahsah. The rest are non-orientable. The second and sixth of each regiment are wild, the rest are tame.
This regiment has doehonnic symmetry.
87. Riddoh - (RID oh) rectified doehon. It has octs and ids.
88. Ciddohdet - (CID oh det) cube-doe-hemidetrat. It has sidhids, octs, and tidects.
89. Dohdet - (DOH det) doe-hemidetrat. It has seihids and tidects.
90. Rihipesh - (RIH hi pesh) rectified ihipesh. It has ids, thahs, and tepeats.
91. Ciddid Hadthippis - (SID id had THIP iss) cube-disdoe-hemidetrat-hemipesquat. It has seihids, thahs, ids, tepeats, and tidects.
92. Dichid Thappis - (DICH id THAP iss) doe-cube-hemidetrat-hemipesquat. It has sidhids, thahs, tepeats, and tidects.
93. Chadditid - (CHAD it id) cube-hemidetrat-doe. It has octs, seihids, and tidects.
94. Dahdittic - (DAH dit ic) doe-hemidetrat-cube. It has thahs, sidhids, and tidects.
This regiment has shexahic symmetry.
95. Rishexah - (RIH shex ah) rectified shexah. It has octs and thats.
96. Chahat - (CHAH hat) cube-hexat-hemiaztrat. It has hohas, octs, and tazts.
97. Hahat - (HAH hat) hexat-hemiaztrat. It has thas and tazts.
98. Ritrihish - (RIH trih hish) rectified trihish. It has thats, thahs, and tehats.
99. Ciddih Hathahs - (SID ih HATH as) cube-dishexat-hemiaztrat-hemihisquat. It has thas, thahs, thats, tehats, and tazts.
100. Hachathahs - (HACH ath as) hexat-cube-hemiaztrat-hemihisquat. It has hohas, thahs, tehats, and tazts.
101. Chath - (CHAD it id) cube-hemiaztrat-hexat. It has octs, thas, and tazts.
102. Hohattic - (DAH dit ic) hexat-hemiaztrat-cube. It has thahs, hohas, and tazts.
This regiment has squahic symmetry.
103. Rocth - (ROCTH) rectified octh. It has squats and coes.
104. Sohahs - (SOH has) squat-oct-hemihisquat. It has chos, squats, and tehats.
105. Ohahs - (OH has) oct-hemihisquat. It has ohos and tehats.
106. Rohah - (ROW hah) rectified ohah. It has coes, shas, and tazts.
107. Siddohahsha - (SID oh ha sha) squat-disoct-hemihisquat-hemiazat. It has chos, shas, coes, tazts, and tehats.
108. Oshahsha - (oh SHA sha) oct-squat-hemihisquat-hemiazat. It has ohos, shas, tazts, and tehats.
109. Shahso - (SHA so) squat-hemihisquat-oct. It has squats, chos, and tehats.
110. Ohahsis - (oh HA sis) oct-hemihisquat-squat. It has shas, ohos, and tehats.
This regiment has squahic or sisquahic symmetry.
13. Squah - (SQUA) square tiling honeycomb. Can be also called rectified sisquah. It has squats and squats.
111. Sahas - (SA has) squat-hemiasquat. It has shas and tezts.
112. Dissahas - (diss AH has) dissquat-hemiasquat. It has shas, squats, and tezts.
113. Hassas - (HASS as) hemiasquat-squat. It has shas and tezts.
114. Rishahsa - (rih SHA sa) rectified shahsa. It has squats, shas, and tezts.
This regiment is the rectification of siddoh.
115. Risdoe - (RIS doe) rectified siddoh. It has dids and peats.
116. Dophahp - (doe FAP) doe-peat-hemihipat. It has sidheis, peats, and phats.
117. Dohahp - (doe HAP) doe-hemihipat. It has gidheis and phats.