# Category 22: Gidipthi Regiment

The gidipthi regiment contains 81 main members plus several fissaries, coincidics, and exotics. This regiment has hyic symmetry. Gidipthi and its other 80 main regiment members have 1440 vertices and 7200 edges. It's verf is a pentagonal podium. It's cells are 120 sissids, 120 ikes, and 120 gaddids. Many of these are extremely complex looking. Gidipthi is one of the 4-D analogues of gaddid. 15 of these are tame, 2 are feral, the rest are wild. Gidipthi members not only have conjugates (which are the padohi members), they also have "reverts", "inflections", and "inflectoverts". The "revert" of a polychoron is the polychoron which has a vertex figure that looks like the upside down version of the original's verf. The "inflection" of a gidipthi member is the one that does the following swap on the faces: ike's triangles - pentagons, gike's triangles - pentagrams, squares - hexagons, decagrams to themselves. The revert of the inflection is the same as the inflection of the revert which we can call the "inflectovert".

## The Main Seven

These first seven are all tame and self-reverted. There are three inflection pairs of orientable members, while the last one is non-orientable and self-inflected. The first four have Wythoffian symbols and can be refered to as "officers" of the regiment. The vertex figures are shown above.

1066. Gidipthi - (gih DIP thee) great dipentary tris120. Its cells are 120 sissids, 120 ikes, and 120 gaddids. Its symbol is o^(o*x*'x). This is the colonel of the regiment.

1067. Gisdipthi - (gis DIP thee) great small dipentary tris120. Its cells are 120 gikes, 120 gads, and 120 gidditdids. Its symbol is o*(o^x*'x). This is one of the sergeants of the regiment.

1068. Gidpixathi - (gid PIK sa thee) great dipentary 600tris120. Its cells are 120 sissids, 120 ikes, 120 tiggies, 600 tuts. Its symbol is (xo^o*'x). This is one of the sergeants of the regiment.

1069. Quipdohi - (QUIP do hi) quasiprismated dis120. Its cells are 120 gikes, 120 gads, 720 pips, and 1200 trips. Its symbol is xo*o^x. This is the conjugate of padohi and therefore it is the lieutenant of this regiment.

1070. Gidpixady - (gid PIX a dee) great dipentary 600dis120. Its cells are 600 tuts, 120 tiggies, and 120 gaddids.

1071. Gidpadiphi - (GID pa DIP thee) great dipentary diprismato120. Its cells are 720 pips, 1200 trips, and 120 gidditdids.

1072. Gidpaxhi - (gid PAK she) great dipentary 600-120. Its cells are 120 ris and 600 choes. This one is excruciatingly complex looking and is full of holes.

## The Wild Eight

These eight are grouped into four pairs of inflections. These are all orientable, wild, and self-reverted. The vertex figures are shown above.

1073. Giddip Dipthix - (GID dip DIP thix) great dipentary disprismatotris120-600. Its cells are 120 sissids, 120 ikes, 600 ohoes, 120 ideds, 720 pips, and 1200 trips.

1074. Gidpixhixthi - (GID pik SHIX thee) great dipentary 600-120-600tris120. Its cells are 120 gikes, 120 gads, 600 coes, 120 radeds, 600 tuts, and 120 tiggies.

1075. Gidpathihix - (gid PATH e hix) great dipentary tris120-120-600. Its cells are 120 sissids, 120 ikes, 600 ohoes, 120 ideds, and 120 gidditdids.

1076. Gidpuxthi - (gid PUX thee) great dipentary 600tetris120. Its cells are 120 gikes, 120 gads, 600 coes, 120 radeds, and 120 gaddids.

1077. Gidpid Hixady - (GID pid HIK sa dee) great dipentary dis120-600dis120. Its cells are 120 sissids, 120 ikes, 600 coes, 120 radeds, and 120 gidditdids.

1078. Gidputhix - (gid POO thix) great dipentary tetris120-600. Its cells are 120 gikes, 120 gads, 600 ohoes, 120 ideds, and 120 gaddids.

1079. Gidpid Phixhi - (GID pid FIK she) great dipentary disprismato120-600-120. Its cells are 720 pips, 1200 trips, 600 ohoes, 120 ideds, and 120 gaddids.

1080. Gidphiddixady - (GID fid DIK sa dee) great dipentary 120dis600dis120. Its cells are 600 tuts, 120 tiggies, 600 coes, 120 radeds, and 120 gidditdids.

## The Self-Inflectoverts

These six are grouped into three pairs of reverts (which are also inflections). These are self-inflectoverted. All of these are non-orientable. The first two are feral, the others are wild. The vertex figures are shown above.

1081. Gicdip Pixthi - (GIK dip PIX thee) great capped dipentary prismato600tris120. Its cells are 120 sissids, 120 gads, 720 pips, 120 tiggies, and 600 choes.

1082. Gibdip Pixthi - (GIB dip PIX thee) great based dipentary prismato600tris120. Its cells are 120 gikes, 120 ikes, 1200 trips, 600 tuts, and 120 ris.

1083. Gidpupthi - (gid PUP thee) great dipentary prismatotetris120. Its cells are 120 sissids, 120 gads, 720 pips, 120 tiggies, and 120 ris.

1084. Gidpip Dixady - (GID pip DIK sa dee) great dipentary prismatodis600dis120. Its cells are 120 gikes, 120 ikes, 1200 trips, 600 tuts, and 600 choes.

1085. Gidphixipthi - (GID fik SIP thee) great dipentary 120-600prismatotris120. Its cells are 120 sissids, 120 gads, 1200 trips, 600 tuts, 120 qrids, and 120 giids.

1086. Gidpid Hipthi - (GID pid HIP thee) great dipentary dis120prismatotris120. Its cells are 120 gikes, 120 ikes, 720 pips, 120 tiggies, 120 qrids, and 120 giids.

## The Great Eight

These eight are grouped into two sets of four. Each set is a revert-inflection set (revin for short), containing a polychoron with its revert, inflection, and inflectovert. The second set has spiky verfs. All of these are tame and non-orientable and have only three types of cells. The vertex figures are shown above.

1087. Gad Phiddix - (gad FID dix) great dipentary 120dis600. Its cells are 120 gikes, 600 tuts, and 600 ohoes.

1088. Gigdipthi - (gig DIP thee) great great dipentary tris120. Its cells are 120 gads, 120 tiggies, and 120 ideds.

1089. Gid Pippady - (gid PIP a dee) great dipentary prismatodis120. Its cells are 120 sissids, 720 pips, and 120 radeds.

1090. Gidpapixhi - (GID pa PIK she) great dipentary prismato600-120. Its cells are 120 ikes, 1200 trips, and 600 coes.

1091. Gind Pippady - (gind PIP pa dee) great spinodipentary prismatodis120. Its cells are 120 gikes, 1200 trips, and 120 girds.

1092. Gind Phiphi - (gind FEE fee) great spinodipentary 120prismato120. Its cells are 120 gads, 720 pips, and 120 girds.

1093. Gandipthi - (gand DIP thee) great spinodipentary tris120. Its cells are 120 sissids, 120 tiggies, and 120 giddies.

1094. Gidphihix - (gid PHI hix) great dipentary 120-120-600. Its cells are 120 ikes, 600 tuts, and 120 giddies.

## The Single Capped Group

These eight form two revin sets of four. The "caps" are the four cells: sissid, gike, ike, and gad (ike and gad can be called bases also), these cells appear as caps or bases on the vertex figure. This group along with the next two groups only have one cap cell. All of these are non-orientable and wild. These have four types of cells. The vertex figures are shown above.

1095. Giddip Phixhi - (GID dip FIK she) great dipentary prismato120-600-120. Its cells are 120 gikes, 720 pips, 600 choes, and 120 giids.

1096. Gidpipthi - (gid PIP thee) great dipentary prismatotris120. Its cells are 120 gads, 1200 trips, 120 ris, and 120 giids.

1097. Gicdappixthi - (GIC da PIX thee) great capped dipentary 600tris120. Its cells are 120 sissids, 600 tuts, 120 ris, and 120 qrids.

1098. Gibdappixthi - (GIB da PIX thee) great based dipentary 600tris120. Its cells are 120 ikes, 120 tiggies, 600 choes, and 120 qrids.

1099. Gide Phixady - (gide FIK sa dee) great invertidipentary 120-600dis120. Its cells are 120 gikes, 120 tiggies, 600 ohoes, and 120 gaddids.

1100. Gide Pixhidy - (GIDE pik SHY dee) great invertidipentary 600-120dis120. Its cells are 120 gads, 600 tuts, 120 ideds, and 120 gaddids.

1101. Gicad Pipithi - (GI kad PIP a thee) great inverticapped dipentary prismatotris120. Its cells are 120 sissids, 1200 trips, 120 radeds, and 120 gidditdids.

1102. Giddip Xappady - (GID dip ZAP a dee) great dipentary 600prismatodis120. Its cells are 120 ikes, 720 pips, 600 coes, and 120 gidditdids.

## The Spike Meisters

These eight have four types of cells and are single-capped like the last group, but with one noticeable change - they have spikey verfs leading to spikey edges. All of these are non-orientable and wild. They form two revin sets. The vertex figures are shown above.

1103. Gidphipdy - (gid FIP dee) great dipentary 120prismatodis120. Its cells are 120 gikes, 1200 trips, 120 ris, and 120 giddies.

1104. Gidphiphix - (gid FEE fix) great dipentary 120prismato120-600. Its cells are 120 gads, 720 pips, 600 choes, and 120 giddies.

1105. Ganc Dapixthi - (GANC da PIX thee) great spinocapped dipentary 600tris120. Its cells are 120 sissids, 120 tiggies, 600 choes, and 120 girds.

1106. Ganb Dapixthi - (GANB da PIX thee) great spinobased dipentary 600tris120. Its cells are 120 ikes, 600 tuts, 120 ris, and 120 girds.

1107. Gidphippixhi - (GID fip PIK she) great dipentary 120prismato600-120. Its cells are 120 gikes, 1200 trips, 600 choes, and 120 giddies.

1108. Gandpid Hiphi - (GAND pid HIF fee) great spinodipentary dis120prismato120. Its cells are 120 gads, 720 pips, 120 ris, and 120 giddies.

1109. Gandupthi - (gand DUP thee) great spinodipentary tetris120. Its cells are 120 sissids, 120 tiggies, 120 ris, and 120 girds.

1110. Gidpid Hiddix - (GID pid HID dix) great dipentary dis120dis600. Its cells are 120 ikes, 600 tuts, 600 choes, and 120 girds.

## The Big Gang

These sixteen have five types of cells. These are wild, non-orientable, and single-capped. These form four revin sets. The vertex figures are shown above.

1111. Gicdiphip Xady - (GIC dif fip ZAY dee) great capped dipentary 120prismato600dis120. Its cells are 120 gikes, 600 tuts, 120 tiggies, 1200 trips, and 120 qrids.

1112. Gibdiphip Xady - (GIB dif fip ZAY dee) great based dipentary 120prismato600dis120. Its cells are 120 gads, 600 tuts, 120 tiggies, 720 pips, and 120 qrids.

1113. Gidpadiphdy - (GID pa DIF dee) great dipentary disprismato120dis120. Its cells are 120 sissids, 720 pips, 1200 trips, 120 tiggies, and 120 giids.

1114. Gidpid Pixady - (GID pid PIK sa dee) great dipentary disprismato600dis120. Its cells are 120 ikes, 720 pips, 1200 trips, 600 tuts, and 120 giids.

1115. Gide Pidhithi - (GIDE pid HITH thee) great invertidipentary dis120tris120. Its cells are 120 gikes, 120 tiggies, 120 radeds, 120 giids, and 120 girds.

1116. Gidpaddy Dixhi - (GID pad dee DIK she) great dipentary dis120dis600-120. Its cells are 120 gads, 600 tuts, 600 coes, 120 giids, and 120 girds.

1117. Gidpithipix - (gid PITH ee pix) great dipentary tris120prismato600. Its cells are 120 sissids, 1200 trips, 600 ohoes, 120 qrids, and 120 giddies.

1118. Gidpiphithi - (gid PIF uh thee) great dipentary prismato120tris120. Its cells are 120 ikes, 720 pips, 120 ideds, 120 qrids, and 120 giddies.

1119. Gidpathixhi - (gid pa THIK she) great dipentary tris120-600-120. Its cells are 120 gikes, 120 tiggies, 600 coes, 120 ris, and 120 gaddids.

1120. Gidpixthix - (gid PIX thix) great dipentary 600tris120-600. Its cells are 120 gads, 600 tuts, 120 radeds, 600 choes, and 120 gaddids.

1121. Gicdip Pidhixhi - (GIC dip pid HIK she) great capped dipentary prismatodis120-600-120. Its cells are 120 sissids, 1200 trips, 120 ideds, 600 choes, and 120 gidditdids.

1122. Gibdip Pidhixhi - (GIB dip pid HIK she) great based dipentary prismatodis120-600-120. Its cells are 120 ikes, 720 pips, 600 ohoes, 120 ris, and 120 gidditdids.

1123. Gicdip Thipix - (GIC dip THI pix) great capped dipentary tris120prismato600. Its cells are 120 gikes, 720 pips, 600 ohoes, 120 ideds, and 120 qrids.

1124. Gibdip Thipix - (GIB dip THI pix) great based dipentary tris120prismato600. Its cells are 120 gads, 1200 trips, 600 ohoes, 120 ideds, and 120 qrids.

1125. Gidphixdahix - (gid FIX da hix) great dipentary 120-600dis120-600. Its cells are 120 sissids, 600 tuts, 600 coes, 120 radeds, and 120 giids.

1126. Gidpaxid Hidy - (gid PAK sid HI dee) great dipentary 600dis120dis120. Its cells are 120 ikes, 120 tiggies, 600 coes, 120 radeds, and 120 giids.

## The Two Capped Quartet

These four have four types of cells, two of which are cap cells. They form a revin set. They are non-orientable and wild. The vertex figures are shown above.

1127. Gidphixady - (gid FIX a dee) great dipentary 120-600dis120. Its cells are 120 gikes, 120 ikes, 600 coes, and 120 girds.

1128. Giddupthi - (gid DUP thee) great dipentary tetris120. Its cells are 120 sissids, 120 gads, 120 radeds, and 120 girds.

1129. Gidphithi - (gid FITH thee) great dipentary 120tris120. Its cells are 120 sissids, 120 gads, 120 ideds, and 120 giddies.

1130. Gidpid Hixhi - (GID pid HIK she) great dipentary dis120-600-120. Its cells are 120 gikes, 120 ikes, 600 ohoes, and giddies.

## The Two Cap Gang

These eight have five types of cells, two of which are cap cells. There are two revin sets here. All of these are non-orientable and wild. The vertex figures are shown above.

1131. Gabdip Xuthi - (GAB dip ZOO thee) great based dipentary 600tetris120. Its cells are 120 gikes, 120 ikes, 600 ohoes, 120 ris, and 120 girds.

1132. Gacdip Xuthi - (GAC dip ZOO thee) great capped dipentary 600tetris120. Its cells are 120 sissids, 120 gads, 120 ideds, 600 choes, and 120 girds.

1133. Gacdupthix - (gac DUP thix) great capped dipentary tetris120-600. Its cells are 120 sissids, 120 gads, 120 radeds, 600 choes, and 120 giddies.

1134. Gabdupthix - (gab DUP thix) great based dipentary tetris120-600. Its cells are 120 gikes, 120 ikes, 600 coes, 120 ris, and 120 giddies.

1135. Gidphiuthi - (gid FYOO thee) great dipentary 120tetris120. Its cells are 120 gikes, 120 gads, 120 ris, 120 girds, and 120 giids.

1136. Gidphixthi - (gid FIX thee) great dipentary 120-600tris120. Its cells are 120 gikes, 120 gads, 600 choes, 120 girds, and 120 giids.

1137. Gidpixhithi - (GID pik SHITH thee) great dipentary 600-120tris120. Its cells are 120 sissids, 120 ikes, 600 choes, 120 giddies, and 120 qrids.

1138. Gidpathidy - (GID pa THI dee) great dipentary tris120dis120. Its cells are 120 sissids, 120 ikes, 120 ris, 120 giddies, and 120 qrids.

## The Orientable Quartet

These four have six types of cells, two of which are cap cells. These form a revin set. All of these are orientable and wild. The vertex figures are shown above.

1139. Giddip Thipox - (GID dip THI pox) great dipentary tetris120prismato600. Its cells are 120 gikes, 120 gads, 720 pips, 120 tiggies, 600 ohoes, and 120 qrids.

1140. Giddip Puthix - (GID dip POO thix) great dipentary prismatotetris120-600. Its cells are 120 gikes, 120 gads, 1200 trips, 600 tuts, 120 ideds, and 120 qrids.

1141. Giddip Xupthi - (GID dip ZUP thee) great dipentary 600prismatotetris120. Its cells are 120 sissids, 120 ikes, 1200 trips, 600 tuts, 120 radeds, and 120 giids.

1142. Giddip Puxthi - (GID dip PUX thee) great dipentary prismato600tetris120. Its cells are 120 sissids, 120 ikes, 720 pips, 120 tiggies, 600 coes, and 120 giids.

## The Ridge Capped Quartet

These four have five types of cells with no cap cells, instead there are the facial ridges of pseudo-cells. These form a revin set. All of these are orientable and wild. The vertex figures are shown above.

1143. Gidpipdyhix - (GID pip DI hix) great dipentary prismatodis120-120-600. Its cells are 720 pips, 120 tiggies, 600 ohoes, 120 qrids, and 120 gidditdids.

1144. Giddip Phidhix - (GID dip FID hix) great dipentary prismato120dis120-600. Its cells are 1200 trips, 600 tuts, 120 ideds, 120 qrids, and 120 gidditdids.

1145. Giddip Pathix - (GID dip PATH ix) great dipentary prismatotris120-600. Its cells are 1200 trips, 600 tuts, 120 radeds, 120 giids, and 120 gaddids.

1146. Giddip Paxthi - (GID dip PAX thee) great dipentary prismato600tris120. Its cells are 720 pips, 120 tiggies, 600 coes, 120 giids, and 120 gaddids.

Below are slices of each of the gidipthis in order, except for the last eight which I have yet to code into POV-Ray.

## Conjugates

Conjugates are in the padohi regiment. They can be found by simple name change rules as follows:

If the first three (or more) letters are amongst these, then make the following swaps: sib-gic, sic-gib, sid-gid, sig-gig, sis-gis, sab-gac, sca-gab, sad-gad, snadd-gand, snid-gind, snic-ganb, snib-ganc, sibed-gicad, snidpid-gandpid, and scaddip-gabdip.

Exceptions: padohi-quipdohi, sicdip pixthi-gicdip pixthi, sibdip pixthi-gibdip pixthi, snidupthi-gandupthi, sabdip xuthi-gabdip xuthi, sacdip xuthi-gacdip xuthi, sacdupthix-gacdupthix, and sabdupthix-gabdupthix.

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