Category 6: Prismatorhombates


These are the prismatorhombates (runcicantellates) and others with similar vertex figures, and their regiments. Their vertex figures are trapezoid pyramids. There are nine regiments of three.


Prich regiment

110. Prich - Prismatorhombated cubic honeycomb, also called runcitruncated cubic honeycomb (or runcicantellated cubic honeycomb). Cells are sircoes, tics, cubes, and ops. Symbol is x4o3x4x.

111. Sepdica (also called spedica) - Small prismatodicubatiapeiratic honeycomb. Cells are soccoes, tics, cubes, and tosquats. Symbol is x4x3o4/3x4*b.

112. Sirpaca - Small rhombiprismatocubatiapeiratic honeycomb. Cells are srohs, ops, and tosquats.


Quiprich regiment

113. Quiprich - Quasiprismatorhombated cubic honeycomb. Cells are sircoes, quiths, cubes, and stops. Symbol is x4o3x4/3x.

114. Mipdica - Medial prismatodicubatiapeiratic honeycomb. Cells are soccoes, quiths, cubes, and qrasquits. Symbol is x4/3x3o4/3x4*b.

115. Mirpaca - Medial rhombiprismatocubatiapeiratic honeycomb. Cells are srohs, stops, and qrasquits.


Gepdica regiment

116. Gepdica - Great prismatodicubatiapeiratic honeycomb. Cells are goccoes, tics, cubes, and qrasquits. Symbol is x4x3o4x4/3*b.

117. Paqrich - Prismatoquasirhombated cubic honeycomb. Cells are quercoes, tics, cubes, and ops. Symbol is x4x3o4/3x.

118. Girpaca - Great rhombiprismatocubatiapeiratic honeycomb. Cells are grohs, ops, and qrasquits.


Gapdica regiment

119. Gapdica - Grand prismatodicubatiapeiratic honeycomb. Cells are goccoes, quiths, cubes, and quitsquats. Symbol is x4/3x3o4x4/3*b.

120. Quipqrich - Quasiprismatoquasirhombated cubic honeycomb. Cells are quercoes, quiths, cubes, and stops. Symbol is x4/3o3x4/3x.

121. Garpaca - Grand rhombiprismatocubatiapeiratic honeycomb. Cells are grohs, stops, and quitsquats.


Sacpaca regiment

122. Sacpaca - Small cubatiprismatocubatiapeiratic honeycomb. Cells are sossas, toes, azips, and quitcoes. Symbol is x3x4o~x4/3*b.

123. Gacpaca - Great cubatiprismatocubatiapeiratic honeycomb. Cells are gossas, toes, azips, and gircoes. Symbol is x3x4x~o4/3*b.

124. Radich - Rhombic apeirodicubatic honeycomb. Cells are sosts, quitcoes, and gircoes.


Dicach regiment

125. Dicach - Dicubatiapeirocubatic honeycomb. Cells are thats, tics, quiths, and cotcoes. Symbol is x3o3x4/3x4*a3*c.

126. Cadich - Cubatiapeirodicubatic honeycomb. Cells are thas, tics, quiths, and satsas. Symbol is x3o3/2x4/3x4*a~*c.

127. Racda - Rhombic cubatidiapeiratic honeycomb. Cells are hohas, cotcoes, and satsas.


Tica regiment

128. Tica - Tricubatiapeiratic honeycomb. Cells are coes, tics, quiths, and qrasquits. Symbol is x3o3x4x4/3*a.

129. Dacdich - Dicubatidicubatic honeycomb. Cells are ohoes, tics, quiths, and cotcoes. Symbol is x3o3/2x4/3x4*a3*c.

130. Rocaca - Rhombic cubaticubatiapeiratic honeycomb. Cells are choes, qrasquits, and cotcoes.


Setcach regiment

131. Setcach - Small tetracubatiapeirocubatic honeycomb. Cells are sircoes, tuts, quitsquats, and quitcoes. Symbol is x3x3o4x4/3*a.

132. Sadcata - Small dicubatitetraapeiratic honeycomb. Cells are soccoes, tuts, quitsquats, and cotcoes. Symbol is x3o4/3x4/3x3*a4*c.

133. Sartich - Small rhombic tricubatic honeycomb. Cells are srohs, quitcoes, and cotcoes.


Gadcata regiment

134. Gadcata - Great dicubatitetraapeiratic honeycomb. Cells are goccoes, tuts, tosquats, and cotcoes. Symbol is x3o4x4x3*a4/3*c.

135. Getcach - Great tetracubatiapeirocubatic honeycomb. Cells are quercoes, tuts, tosquats, and gircoes. Symbol is o3x3x4x4/3*a.

136. Gartich - Great rhombic tricubatic honeycomb. Cells are grohs, cotcoes, and gircoes.


Conjugates

The following honeycombs are self conjugate: radich, dicach, cadich, racda, tica, dacdich, and rocaca.

The following form conjugate pairs: prich - quipqrich, sepdica - gapdica, sirpaca - garpaca, quiprich - paqrich, mipdica - gepdica, mirpaca - girpaca, sacpaca - gacpaca, setcach - getcach, sadcata - gadcata, sartich - gartich.

The following form quasi-conjugate pairs (one set of octagons - octagrams gets swapped, but not the other): prich - quiprich, prich - paqrich, sepdica - mipdica, sepdica - gepdica, sirpaca - mirpaca, sirpaca - girpaca, quiprich - quipqrich, mipdica - gapdica, mirpaca - garpaca, gepdica - gapdica, paqrich - quipqrich, girpaca - garpaca.


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