Category 5: Pentagonal Rectates


This category deals with the rox army, rox being the rectified 600-cell. There are four regiments here: rox, righi, ragishi, and rigfix - each having 15 members. Each regiment also has 2 coincidic cases and 5 exotic cases. The verfs of these are various facetings of the pentagonal prism. Each polychoron here has 720 vertices and has hyic symmetry. Rox is the only convex case in this category. In each regiment, the first 7 are tame, the rest are wild. Only the ones with toroidal verfs (sriphi, mriphi, griphi, and graphi) are non-orientable, the others are orientable. For the non-orientable ones (except sriphi) and those that contain giids or qrids, the piece counts and LOCs may no longer be accurate due to neo-filling. Following is a list of the 60 pentagonal rectates.
Rox Regiment Slices

Rox Regiment

Rox Regiment Verfs

This regiment can contain any of the following cells: 120 ikes, 120 gads, 600 octs, 120 ids, 720 pips, 120 tids, 120 srids, 120 saddids, and 120 sirds. Rox's symbol is oxo^o.

73. Rox - (ROCKS) rectified hexacosachoron, also called icosahedral hecatonicosihexacosichoron (George Olshevsky). Its cells are ikes and octs. Its verf is a pip (pentagonal prism). It has 720 pieces of two types, LOC = 3. It is convex and semiregular.

74. Rofix - (RO fix) rectified fix. Its cells are gads and ids. Its verf is a star prism. Its symbol is o*o^xo. It has 2520 pieces of two types, LOC = 11.

75. Sophi - (SO fee) small prismato 120-cell. Its cells are gads and pips. Its verf is a star antiprism. It has 10920 pieces of three types, LOC = 21.

76. Sprapivady - (sprap IV a dee) small pentagonal retroprismatoverted dis120-cell. Its cells are ikes and tids. Its verf is a pentagon retroprism. This polychoron has an interesting appearance. It has 114,120 pieces of 14 types, LOC = 274.

77. Frox - (FROCKS) facetorectified 600-cell. Cells are ids and pips, pseudo cells are pseudo-gads, and pseudo-thahs. Its verf has a hole in it. It has 40680 pieces of ten types, LOC = 80.

78. Rixhi - (RIK she) retroinverted 600-120. Cells are ikes and tids, it also has pseudo-ikes. Its verf is an inverted pip. It has 17400 pieces of four types, LOC = 38. The ike shaped craters have an interesting surprise inside.

79. Sriphi - (SRIF fee) small retropental 120-cell. Its cells are 120 sirds, it is a noble uniform polychoron. Its verf is a pentagonal stephenoid. It has 52800 pieces of 8 types, LOC = 93. It is somewhat loopy looking.

80. Ipixady - (i PIK sa dee) invertipental 600dis120. Its cells are gads, octs, and saddids. Its verf looks like a star capped pip. It has 17520 pieces of five types, LOC = 33.

81. Lifpipixhi - (LIF pih PIK she) polar facetopental prismato600-120. Its cells are octs, saddids, and pips, it also has 120 pseudo ike+gads. Its verf is a polar faceted pip. It has 34680 pieces of 8 types, LOC = 62.

82. Nipixady - (ni PIK sa dee) interceptipental 600dis120. Its cells are gads, octs, and srids. Its verf looks like a star capped pip. It has 17520 pieces of five types, LOC = 33. Nipixady and ipixady are copy cats.

83. Som Fapathi - (som FAP a thee) small omnicircumfacetopental triakis120. Cells are ikes, ids, and srids, it also has 600 pseudo-octs with diagonal squares (called oct+4 for short). Verf is a pip with the squares replaced with "windows". It has 19320 pieces of five types, LOC = 33.

84. Sofapathi - (so FAP a thee) small omnifacetopental triakis120. Its cells are ids, tids, and srids, it has pseudo ike+gads and pseudo oct+4's. Its verf is a completely faceted pip. It has 53280 pieces of 11 types, LOC = 92.

85. Smiffipathi - (smif FIP uh thee) small circumfacetopental triakis120. Its cells are ikes, ids, and saddids, it has pseudo octs. Its verf looks like a pip with the squares sunk in. It has 4920 pieces in three types, LOC = 13.

86. Paphiny - (paf FI ne) pental prismato120intercepted 120. Its cells are ikes, pips, and saddids, it also has pseudo-thahs. Its verf is a faceting of pip. It has 13320 pieces of four types, LOC = 23.

87. Sirphinady - (sir FINE a dee) small inverted retropental 120intercepted dis120. Its cells are gads, tids, and srids, it also has pseudo-pips and pseudo-thahs. Its verf is a pip faceting. It has 16920 pieces of four types, LOC = 29.


Righi Regiment

Righi Regiment Verfs

This regiment is based off of the rectified gohi, which has the symbol o^x*o^o. This regiment contains the following potential cells: 120 sissids, 120 gikes, 120 dids, 120 ids, 600 tuts, 120 tigids, 120 siids, 120 sidditdids, and 120 siddies.

88. Righi - (RIG hi) rectified gohi. Its cells are sissids and dids. Its verf is a long pip. This polychoron has 3720 pieces of two types, LOC = 14.

89. Raghi - (RAG hi) rectified gahi. Its cells are gikes and ids, its symbol is o*ox^o. It has a long stip verf. It has 21720 pieces of four types, LOC = 69.

90. Papvixhi - (pap VIK she) pentagramal antiprismatoverted 600-120. Its cells are gikes and tuts. Its verf is a long stap (star antiprism). It has 32520 pieces of five types, LOC = 86.

91. Giprapivady - (GIH prap IV a dee) great pentagonal retroprismatoverted dis120. Its cells are sissids and tigids. Its verf is a long pentagon retroprism. It has 46920 pieces of 7 types, LOC = 101.

92. Froghi - (FROG hi) facetorectified gohi. Its cells are ids and tuts, it also has pseudo-gikes and pseudo-gidheis. Its verf has a hole. It has 503,040 pieces of 43 types, LOC = 1197.

93. Ridhei - (RID hi) retroinverted dis120. Its cells are dids and tigids, it also has pseudo-sissids. Its verf is a long inverted pip. It has 13800 pieces of five types, LOC = 34.

94. Mriphi - (MRIF fee) medial retropental 120. Its cells are 120 siddies, this polychoron is noble. Its verf is a long pentagonal stephanoid. It has 113,040 pieces of 12 types, LOC = 278.

95. Sipathi - (SIPE a thee) small invertipental triakis120. Its cells are gikes, dids, and sidditdids. Its verf is a long star capped pip. It has 97320 pieces of 11 types, LOC = 202.

96. Lifpixady - (lif PIK sa dee) polar facetopental 600dis120. Its cells are dids, tuts, and sidditdids, it also has pseudo-sissid+gikes. Its verf is a long polar faceted pip. It has 364,080 pieces of 38 types, LOC = 647.

97. Snipathi - (SNIPE a thee) small interceptipental triakis120. Its cells are gikes, dids, and siids, it is a copy cat of sipathi. Its verf is a long star capped pip. It has 97320 pieces of 11 types, LOC = 202.

98. Mom Fapathi - (mom FAP a thee) medial omnicircumfacetopental triakis120. Its cells are sissids, ids, and siids, it also has pseudo did+6's. Its verf is a long omnicircumfaceted pip. "Mommy" has 79320 pieces of 8 types, LOC = 155.

99. Gofapathi - (GO fap a thee) great omnifacetopental triakis120. Its cells are ids, siids, and tigids, it also has pseudo sissid+gikes and pseudo did+6's. Its verf is a long omnifaceted pip. It has 439,680 pieces of 44 types, LOC = 788.

100. Mim Fipathi - (mim FIP a thee) medial circumfacetopental triakis120. Its cells are sissids, ids, and sidditdids, it also has pseudo-dids. Its verf looks like a long pip with the rectangles buckled in. It has 28920 pieces of five types, LOC = 75.

101. Pixhiny - (pik SHINE nee) pental 600-120intercepted 120. Its cells are sissids, tuts, and sidditdids, it also has pseudo-sidheis. Its verf is a faceting of a long pip. It has 32520 pieces of five types, LOC = 72.

102. Girphinady - (gir FINE a dee) great inverted retropental 120intercepted dis120. Its cells are gikes, siids, and tigids. Its verf is a star capped faceting of a long pip. It has 122,520 pieces of 13 types, LOC = 245.


Ragishi Regiment

Ragishi Regiment Verfs

This regiment is based off of the rectified gishi, which has the symbol o*xo^o. This regiment contains the following potential cells: 120 ikes, 120 gads, 120 gids, 120 dids, 120 quit sissids, 600 tuts, 120 gidditdids, 120 giids, and 120 giddies.

103. Ragishi - (ra GISH shee) rectified gishi. Its cells are ikes and gids. Its verf is a flat pentagon prism. It has 5160 pieces of three types, LOC = 20.

104. Ragashi - (RAG a shee) rectified gashi. Its cells are gads and dids, its symbol is o*x^o*o. Its verf is a flat stip. It has 37440 pieces of five types, LOC = 128.

105. Spapivady - (spap IV a dee) small pentagramal antiprismatoverted dis120. Its cells are gads and quit sissids. Its verf is a flat stap. It has 32640 pieces of five types, LOC = 76.

106. Prap Vixhi - (prap VIK she) pentagonal retroprismatoverted 600-120. Its cells are ikes and tuts. Its verf is a flat pentagon retroprism. This polychoron looks like it has suction cups all over it. It has 927,840 pieces with 78 types, LOC = 2562 - this is the winner of the complexity prize in this category.

107. Frogshi - (FROG shi) facetorectified gishi. Its cells are dids and quit sissids, it also has pseudo-gads and pseudo-gidhids. It has a hole in the verf. It has 137,040 pieces of 15 types, LOC = 353.

108. Rihix - (RI hix) retroinverted 120-600. Its cells are gids and tuts, it also has pseudo-ikes. Its verf is a flat inverted pip. It has 10920 pieces of three types, LOC = 32.

109. Griphi - (GRIF fee) great retropental 120. Its cells are 120 giddies, it is noble. Its verf is a flat stephanoid, this polychoron probably looks loopy. It has 93600 pieces of ten types, LOC = 272.

110. Mipathi - (MIPE a thee) medial invertipental triakis120. Its cells are gads, gids, and giids. Its verf is a flat star capped pip. It has 41160 pieces of 8 types, LOC = 144.

111. Sliffipathi - (slif FIP a thee) small polar facetopental triakis120. Its cells are gids, giids, and quit sissids, it also has pseudo-ike+gads. Its verf is a flat polar faceted pip. It has 43320 pieces of 7 types, LOC = 102.

112. Minnipathi - (min IP a thee) medial interceptipental triakis120. Its cells are gads, gids, and gidditdids, it is a copy cat of mipathi. Its verf is a flat star capped pip. It has 41160 pieces with 8 types, LOC = 144.

113. Gom Fapathi - (gom FAP a thee) great omnicircumfacetopental triakis120. Its cells are ikes, gids, and gidditdids, it also has pseudo-gid+10/3's. Its verf is a flat omnicircumfaceted pip. It has 218,640 pieces of 21 types, LOC = 485.

114. Ofapaxady - (OAF a PAK sa dee) omnifacetopental 600dis120. Its cells are dids, tuts, and gidditdids, it also has pseudo-ike+gads and pseudo-gid+10/3's. Its verf is a flat omnifaceted pip. This polychoron is very intricate. It has 290,640 pieces of 29 types, LOC = 703.

115. Gam Fipathi - (gam FIP a thee) great circumfacetopental triakis120. Its cells are ikes, dids, and giids, it also has pseudo-gids. It verf is a flat pip with the rectangles buckled in. It has 175,440 pieces of 17 types, LOC = 464.

116. Spidhiny - (spid HI nee) small pental dis120intercepted 120. Its cells are ikes, giids, and quit sissids. Its verf is a flat pip faceting. It has 41040 pieces in 8 types, LOC = 89.

117. Irp Xanady - (urp ZAN a dee) inverted retropental 600intercepted dis120. Its cells are gads, tuts, and gidditdids. Its verf is a flat star capped pip faceting. It has 243,840 pieces with 27 types, LOC = 606.


Rigfix Regiment

Rigfix Regiment Verfs

This regiment is based off of the rectified gofix, which has the symbol ox*o^o. This regiment contains the following potential cells: 120 sissids, 120 gikes, 120 gids, 120 octs, 120 quit gissids, 600 stips, 120 gaddids, 120 qrids, and 120 girds.

118. Rigfix - (RIG fix) rectified gofix. Its cells are sissids and gids. Its verf is a pentagon prism. It has 5040 pieces with two types, LOC = 24.

119. Raggix - (RAG gix) rectified gax. Its cells are gikes and octs, its symbol is oxo*o. Its verf is a stip. It has 73440 pieces in eight types, LOC = 272.

120. Gippapivady - (GIH pap IV a dee) great pentagramal antiprismatoverted dis120. Its cells are gikes and quit gissids. Its verf is a stap. It has 23040 pieces with three types, LOC = 46.

121. Quiphi - (KWIF fee) quasiprismato120. Its cells are sissids and stips. Its verf is a pentagon retroprism. It has 767,040 pieces in 63 types, LOC = 2423 - the second place winner.

122. Frogfix - (FROG fix) facetorectified gofix. Its cells are octs and quit gissids, it also has pseudo-gikes and pseudo-geihids. It has a hole in the verf. It has 569,040 pieces with 49 types - surely enough to fix your frogs with, LOC = 1470.

123. Ripahi - (RIPE a hi) retroinverted prismato120. Its cells are gids and stips, it also has pseudo-sissids. Its verf is an inverted pip. It has 92880 pieces with 13 types, LOC = 184.

124. Graphi - (GRAF fee) grand retropental 120. Its cells are 120 girds, it is noble. Its verf is a stephanoid. It has 189,600 pieces in 18 types, LOC = 462.

125. Gipathi - (GIPE a thee) great invertipental triakis120. Its cells are gikes, gids, and qrids. Its verf is a star capped pip. It has 98640 pieces in 12 types, LOC = 226.

126. Gliffipathi - (glif FIP a thee) great polar facetopental triakis120. Its cells are gids, qrids, and quit gissids, it also has pseudo-sissid+gikes. Its verf is a polar faceted pip. "Ol' gliff" has 100,080 pieces in 13 types, LOC = 232.

127. Ganipathi - (ga NIP a thee) great interceptipental triakis120. Its cells are gikes, gids, and gaddids, it is a copy cat of gipathi. Its verf is a star capped pip. It has 98640 pieces of 12 types, LOC = 226.

128. Omfapaxady - (OM fa PAK sa dee) omnicircumfacetopental 600dis120. Its cells are sissids, gids, and gaddids, it also has pseudo-gid+10/3's. Its verf is an omnicircumfaceted pip. It has 87840 pieces of 9 types, LOC = 236.

129. Ofpipixhi - (OFF pa PIK she) omnifacetopental prismato600-120. Its cells are octs, stips, and gaddids, it also has pseudo-sissid+gikes and pseudo-gid+10/3's. Its verf is an omnifaceted pip. This polychoron is very intricate with 253,440 pieces in 24 types, LOC = 628.

130. Mif Pixady - (mif PIK sa dee) circumfacetopental 600dis120. Its cells are sissids, octs, and qrids, it also has pseudo-gids. It verf is a pip with the rectangles buckled in. It has 116,640 pieces with 11 types, LOC = 330.

131. Gipdohiny - (GIP do hi nee) great pental dis120intercepted 120. Its cells are sissids, qrids, and quit gissids. Its verf is a pip faceting. It has 30240 pieces coming in four types, LOC = 60.

132. Irp Panady - (urp PAN a dee) inverted retropental prismatointercepted dis120. Its cells are gikes, stips, and gaddids. Its verf is a star capped pip faceting. It has 140,640 pieces with 17 types, LOC = 356.


Below are slices of the members of Category 5, in the same order as in the text. Those with giids or qrids have yet to be added in.

Sample Slices of the Rox Army


Conjugates

Below shows how the pentagonal rectates pair up as conjugates.

rox-raggix, rofix-rigfix, sophi-quiphi, sprapivady-gippapivady, frox-ripahi, rixhi-frogfix, sriphi-graphi, ipixady-omfapaxady, lifpipixhi-ofpipixhi, nipixady-mif pixady, som fapathi-gipathi, sofapathi-gliffipathi, smiffipathi-ganipathi, paphiny-irp panady, sirphinady-gipdohiny, righi-ragashi, raghi-ragishi, papvixhi-prap vixhi, giprapivady-spapivady, froghi-rihix, ridhei-frogshi, mriphi-griphi, sipathi-gom fapathi, lifpixady-ofapaxady, snipathi-gam fipathi, mom fapathi-mipathi, gofapathi-sliffipathi, mim fipathi-minnipathi, pixhiny-irp xanady, girphinady-spidhiny.

Category 4 --- back to Polychoron Page --- Category 6