There are 32 square rectates, divided up into 3 regiments of 9, 1 regiment of 5, and 1 regiment of 5. One of the 37 is a repeat, meaning there are 36 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. Chadditid - (CHAD it id) cube-hemidetrat-doe. It has sidhids, octs, and tidects.
89. Dahdit - (DAH dit) doe-hemidetrat. It has seihids and tidects.
90. Ridhipesh - (RID hi pesh) rectified dihipesh. It has ids, thahs, and tepeats.
91. Ridade - (Ri DAYD) rectified dade. It has thahs, sidhids, and tidects.
92. Rhacud - (RA kud) rectified hacud. It has octs, seihids, and tidects.
93. Diddic Hedathips - (DID ick he DATH ips) disdoe-cube-hemidetrat-hemipesquat. It has sidhids, seihids, thahs, ids, tepeats, and tidects.
94. Ciddid Hadthippis - (SID id had THIP iss) cube-disdoe-hemidetrat-hemipesquat. It has seihids, thahs, ids, tepeats, and tidects.
95. Dichid Thappis - (DICH id THAP iss) doe-cube-hemidetrat-hemipesquat. It has sidhids, thahs, tepeats, and tidects.
This regiment has shexahic symmetry.
96. Rishexah - (RIH shex ah) rectified shexah. It has octs and thats.
97. Chath - (CHAH hat) cube-hemiaztrat-hexat. It has hohas, octs, and tazts.
98. Hihat - (HI hat) hexat-hemiaztrat. It has thas and tazts.
99. Ritrihish - (RIH trih hish) rectified trihish. It has thats, thahs, and tehats.
100. Rhazh - (RAZH) rectified hazh. It has thahs, hohas, and tazts.
101. Rhaca - (RACK ah) rectified haca. It has octs, thas, and tazts.
102. Dhachat Hihis - (DACH at HI his) dishexat-cube-hemiaztrat-hemihisquat. It has thas, hohas, thahs, tehats, and tazts.
103. Ciddih Hathahs - (SID ih HATH as) cube-dishexat-hemiaztrat-hemihisquat. It has thas, thahs, thats, tehats, and tazts.
104. Hachathahs - (HACH ath as) hexat-cube-hemiaztrat-hemihisquat. It has hohas, thahs, tehats, and tazts.
This regiment has squahic symmetry.
105. Rocth - (ROCTH) rectified octh. It has squats and coes.
106. Sohahs - (SOH has) squat-oct-hemihisquat. It has chos, squats, and tehats.
107. Ohahs - (OH has) oct-hemihisquat. It has ohos and tehats.
108. Rohah - (ROW hah) rectified ohah. It has coes, shas, and tazts.
109. Ricish - (RI kish) oct-hemihisquat-squat. It has coes, ohos, and tehats.
110. Risassoh - (ri SASS oh) squat-hemihisquat-oct. It has squats, chos, and tehats.
113. Doshahsha - (doh SHA sha) disoct-squat-hemihisquat-hemiazat. It has ohos, chos, shas, tazts, and tehats.
112. Siddohahsha - (SID oh ha sha) squat-disoct-hemihisquat-hemiazat. It has chos, shas, coes, tazts, and tehats.
113. Oshahsha - (oh SHA sha) oct-squat-hemihisquat-hemiazat. It has ohos, shas, tazts, 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.
114. Tasthassa - (TAS thas ah) trissquat-trishemisquazat. It has shas and tezts.
115. Tasdahsa - (TAS da sa) trissquat-dishemisquazat. It has shas, squats, and tezts.
116. Dasdahsa - (DAS da sa) dissquat-dishemisquazat. It has shas and tezts.
117. Rishahsa - (rih SHA sa) rectified shahsa. It has squats, shas, and tezts.
This regiment is the rectification of siddoh.
118. Rissidoh - (ris SID oh) rectified siddoh. It has dids and peats.
119. Dophahp - (doe FAP) doe-peat-hemihipat. It has sidheis, peats, and phats.
120. Dohahp - (doe HAP) doe-hemihipat. It has gidheis and phats.
121. Ridoph - (RID oaf) rectified doph. It has sidheis, dids, and phats.
122. Rippiph - (RIP if) rectified pepiph. It has gidheis, peats, and phats.